{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<img src=\"http://hilpisch.com/tpq_logo.png\" alt=\"The Python Quants\" width=\"35%\" align=\"right\" border=\"0\"><br>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Python for Finance (2nd ed.)\n",
    "\n",
    "**Mastering Data-Driven Finance**\n",
    "\n",
    "&copy; Dr. Yves J. Hilpisch | The Python Quants GmbH\n",
    "\n",
    "<img src=\"http://hilpisch.com/images/py4fi_2nd_shadow.png\" width=\"300px\" align=\"left\">"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Mathematical Tools"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Approximation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from pylab import plt, mpl"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "plt.style.use('seaborn')\n",
    "mpl.rcParams['font.family'] = 'serif'\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "uuid": "2326c3ad-f244-4f48-8b68-851bd2347d57"
   },
   "outputs": [],
   "source": [
    "def f(x):\n",
    "    return np.sin(x) + 0.5 * x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "def create_plot(x, y, styles, labels, axlabels):\n",
    "    plt.figure(figsize=(10, 6))\n",
    "    for i in range(len(x)):\n",
    "        plt.plot(x[i], y[i], styles[i], label=labels[i])\n",
    "        plt.xlabel(axlabels[0])\n",
    "        plt.ylabel(axlabels[1])\n",
    "    plt.legend(loc=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "uuid": "c09f73d2-c2a5-4c6d-a2f1-08a191378417"
   },
   "outputs": [],
   "source": [
    "x = np.linspace(-2 * np.pi, 2 * np.pi, 50)  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "uuid": "96d2bd1b-8883-486d-920d-b610aeb076a8"
   },
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "create_plot([x], [f(x)], ['b'], ['f(x)'], ['x', 'f(x)'])\n",
    "# plt.savefig('../../images/ch11/math_01.png');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Regression"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Monomials as Basis Functions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "res = np.polyfit(x, f(x), deg=1, full=True)  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([ 4.28841952e-01, -4.31775426e-17]),\n",
       " array([21.03238686]),\n",
       " 2,\n",
       " array([1., 1.]),\n",
       " 1.1102230246251565e-14)"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "res  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "uuid": "ace90420-7219-4227-8210-bf107f556726"
   },
   "outputs": [],
   "source": [
    "ry = np.polyval(res[0], x)  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "uuid": "c0667d3e-a48a-413d-b250-5e0d3b58275e"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "create_plot([x, x], [f(x), ry], ['b', 'r.'],\n",
    "            ['f(x)', 'regression'], ['x', 'f(x)'])\n",
    "# plt.savefig('../../images/ch11/math_02.png');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "uuid": "096bb07a-55f7-45de-8734-2a76d8749d53"
   },
   "outputs": [],
   "source": [
    "reg = np.polyfit(x, f(x), deg=5)\n",
    "ry = np.polyval(reg, x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "uuid": "5e17309e-e8e2-4df9-b841-0f57d983b89e"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "create_plot([x, x], [f(x), ry], ['b', 'r.'],\n",
    "            ['f(x)', 'regression'], ['x', 'f(x)'])\n",
    "# plt.savefig('../../images/ch11/math_03.png');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "uuid": "67b14a21-e8f2-4dd4-a43b-0d232f2b4055"
   },
   "outputs": [],
   "source": [
    "reg = np.polyfit(x, f(x), 7)\n",
    "ry = np.polyval(reg, x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "uuid": "e600b6be-4cf2-4212-807a-7f397f081e98"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "False"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.allclose(f(x), ry)  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "uuid": "bc6918fe-f520-483c-94eb-41dd89abfa70"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.0017769134759517671"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.mean((f(x) - ry) ** 2)  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "uuid": "053752b7-7eb3-4d93-acdf-69874ceada12"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "create_plot([x, x], [f(x), ry], ['b', 'r.'],\n",
    "            ['f(x)', 'regression'], ['x', 'f(x)'])\n",
    "# plt.savefig('../../images/ch11/math_04.png');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Individual Basis Functions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "uuid": "b4f05890-56e0-4f29-9d61-bd9948ad8af0"
   },
   "outputs": [],
   "source": [
    "matrix = np.zeros((3 + 1, len(x)))  \n",
    "matrix[3, :] = x ** 3  \n",
    "matrix[2, :] = x ** 2  \n",
    "matrix[1, :] = x  \n",
    "matrix[0, :] = 1  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "uuid": "c8963eee-4bc8-4ef2-a172-d4b64fd065a3"
   },
   "outputs": [],
   "source": [
    "reg = np.linalg.lstsq(matrix.T, f(x), rcond=None)[0]  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "uuid": "efd077d1-9c8a-4961-be95-400f83cd679e"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.    ,  0.5628, -0.    , -0.0054])"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "reg.round(4)  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "uuid": "efb7b252-d0f8-4263-b2be-4d9588ab06a7"
   },
   "outputs": [],
   "source": [
    "ry = np.dot(reg, matrix)  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "uuid": "1b1953fe-83a2-436b-8cd4-69c5abf6d2e1"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "create_plot([x, x], [f(x), ry], ['b', 'r.'],\n",
    "            ['f(x)', 'regression'], ['x', 'f(x)'])\n",
    "# plt.savefig('../../images/ch11/math_05.png');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "matrix[3, :] = np.sin(x)  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "reg = np.linalg.lstsq(matrix.T, f(x), rcond=None)[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "uuid": "86f9a92c-600d-4515-b34d-20c9f35a86b0"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0. , 0.5, 0. , 1. ])"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "reg.round(4)  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "uuid": "ac77ef01-8abe-4b99-8f92-8325a396ff2c"
   },
   "outputs": [],
   "source": [
    "ry = np.dot(reg, matrix)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "uuid": "02481bd5-c737-46bc-9b90-5554fcad8745"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.allclose(f(x), ry)  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "uuid": "6bf80137-3a52-483b-a557-b092bbf23b36"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "9.145856119906106e-31"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.mean((f(x) - ry) ** 2)  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "uuid": "58d9db31-5885-4fba-8ae7-2e962a0963ca"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "create_plot([x, x], [f(x), ry], ['b', 'r.'],\n",
    "            ['f(x)', 'regression'], ['x', 'f(x)'])\n",
    "# plt.savefig('../../images/ch11/math_06.png');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Noisy Data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "uuid": "75d3a6a6-a940-4a49-b35d-29f21880ab95"
   },
   "outputs": [],
   "source": [
    "xn = np.linspace(-2 * np.pi, 2 * np.pi, 50)  \n",
    "xn = xn + 0.15 * np.random.standard_normal(len(xn))  \n",
    "yn = f(xn) + 0.25 * np.random.standard_normal(len(xn))  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "uuid": "f6f9c05f-1f96-48ee-aaca-f4d80c3d3ac5"
   },
   "outputs": [],
   "source": [
    "reg = np.polyfit(xn, yn, 7)\n",
    "ry = np.polyval(reg, xn)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "uuid": "9a475222-3bfd-4300-951b-94e60792c6da"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "create_plot([x, x], [f(x), ry], ['b', 'r.'],\n",
    "            ['f(x)', 'regression'], ['x', 'f(x)'])\n",
    "# plt.savefig('../../images/ch11/math_07.png');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Unsorted Data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "uuid": "8ea85cdb-47f2-4967-b684-7894d9964e76"
   },
   "outputs": [],
   "source": [
    "xu = np.random.rand(50) * 4 * np.pi - 2 * np.pi  \n",
    "yu = f(xu)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "uuid": "0034edf5-1cef-4eea-be44-c69103fe6eb2"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 3.17 -2.36  0.46 -4.06 -0.47  4.42 -1.42  5.8  -0.28 -6.01]\n",
      "[ 1.56 -1.88  0.68 -1.24 -0.69  1.25 -1.7   2.43 -0.42 -2.73]\n"
     ]
    }
   ],
   "source": [
    "print(xu[:10].round(2))  \n",
    "print(yu[:10].round(2))  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "uuid": "d7f5f003-1cb8-4432-a8d6-cb4bef1a101a"
   },
   "outputs": [],
   "source": [
    "reg = np.polyfit(xu, yu, 5)\n",
    "ry = np.polyval(reg, xu)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "uuid": "40177962-0363-479c-bdbd-451a4c043060"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "create_plot([xu, xu], [yu, ry], ['b.', 'ro'],\n",
    "            ['f(x)', 'regression'], ['x', 'f(x)'])\n",
    "# plt.savefig('../../images/ch11/math_08.png');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Multiple Dimensions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "uuid": "82b95a7b-9e3e-4dc8-b313-1af775b06b8b"
   },
   "outputs": [],
   "source": [
    "def fm(p):\n",
    "    x, y = p\n",
    "    return np.sin(x) + 0.25 * x + np.sqrt(y) + 0.05 * y ** 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [],
   "source": [
    "x = np.linspace(0, 10, 20)\n",
    "y = np.linspace(0, 10, 20)\n",
    "X, Y = np.meshgrid(x, y)  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "uuid": "b03b67ac-f7df-41d1-9dab-1e074e8738fa"
   },
   "outputs": [],
   "source": [
    "Z = fm((X, Y))\n",
    "x = X.flatten()  \n",
    "y = Y.flatten()  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "uuid": "52a91ef7-33c4-4de1-b69b-ea4d740aa252"
   },
   "outputs": [],
   "source": [
    "from mpl_toolkits.mplot3d import Axes3D  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "uuid": "52a91ef7-33c4-4de1-b69b-ea4d740aa252"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.colorbar.Colorbar at 0x7f866a389d50>"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x432 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(10, 6))\n",
    "ax = fig.gca(projection='3d')\n",
    "surf = ax.plot_surface(X, Y, Z, rstride=2, cstride=2,\n",
    "                       cmap='coolwarm', linewidth=0.5,\n",
    "                       antialiased=True)\n",
    "ax.set_xlabel('x')\n",
    "ax.set_ylabel('y')\n",
    "ax.set_zlabel('f(x, y)')\n",
    "fig.colorbar(surf, shrink=0.5, aspect=5)\n",
    "# plt.savefig('../../images/ch11/math_09.png');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "uuid": "5918f2cf-3ead-4b80-980e-4a375ee159db"
   },
   "outputs": [],
   "source": [
    "matrix = np.zeros((len(x), 6 + 1))\n",
    "matrix[:, 6] = np.sqrt(y)  \n",
    "matrix[:, 5] = np.sin(x)  \n",
    "matrix[:, 4] = y ** 2\n",
    "matrix[:, 3] = x ** 2\n",
    "matrix[:, 2] = y\n",
    "matrix[:, 1] = x\n",
    "matrix[:, 0] = 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "uuid": "b9eb74bd-9280-4d8b-ae7d-8853911389cb"
   },
   "outputs": [],
   "source": [
    "reg = np.linalg.lstsq(matrix, fm((x, y)), rcond=None)[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [],
   "source": [
    "RZ = np.dot(matrix, reg).reshape((20, 20))  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "scrolled": true,
    "uuid": "096451ce-173a-43b5-b81f-9dac26df2702"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.colorbar.Colorbar at 0x7f866a08e690>"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x432 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(10, 6))\n",
    "ax = fig.gca(projection='3d')\n",
    "surf1 = ax.plot_surface(X, Y, Z, rstride=2, cstride=2,\n",
    "            cmap=mpl.cm.coolwarm, linewidth=0.5,\n",
    "            antialiased=True)  \n",
    "surf2 = ax.plot_wireframe(X, Y, RZ, rstride=2, cstride=2,\n",
    "                          label='regression')  \n",
    "ax.set_xlabel('x')\n",
    "ax.set_ylabel('y')\n",
    "ax.set_zlabel('f(x, y)')\n",
    "ax.legend()\n",
    "fig.colorbar(surf, shrink=0.5, aspect=5)\n",
    "# plt.savefig('../../images/ch11/math_10.png');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Interpolation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "uuid": "5e345542-f425-4630-9eae-0a446927ad73"
   },
   "outputs": [],
   "source": [
    "import scipy.interpolate as spi  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "uuid": "20200433-3e90-4bb6-be5a-8e6a1360989e"
   },
   "outputs": [],
   "source": [
    "x = np.linspace(-2 * np.pi, 2 * np.pi, 25)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "uuid": "6e3caa90-2a2a-4429-8536-ab25091a5640"
   },
   "outputs": [],
   "source": [
    "def f(x):\n",
    "    return np.sin(x) + 0.5 * x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {
    "uuid": "afdb9c45-1b12-4358-ba3e-a1bc3c4d32db"
   },
   "outputs": [],
   "source": [
    "ipo = spi.splrep(x, f(x), k=1)  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "uuid": "7217594a-3398-4dfd-9d16-f90ee0f24bd9"
   },
   "outputs": [],
   "source": [
    "iy = spi.splev(x, ipo)  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {
    "uuid": "b9cacc73-786b-4c6b-ad5f-e4d22729c17e"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.allclose(f(x), iy)  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {
    "uuid": "89d96d0e-dabd-490f-acad-15bba904b546"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "create_plot([x, x], [f(x), iy], ['b', 'ro'],\n",
    "            ['f(x)', 'interpolation'], ['x', 'f(x)'])\n",
    "# plt.savefig('../../images/ch11/math_11.png');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {
    "uuid": "3daf1f42-54d8-4150-aab6-5188d1c23bdb"
   },
   "outputs": [],
   "source": [
    "xd = np.linspace(1.0, 3.0, 50)  \n",
    "iyd = spi.splev(xd, ipo)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {
    "uuid": "7ba1134b-ac71-4c3a-a0fc-b644c59effc6"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "create_plot([xd, xd], [f(xd), iyd], ['b', 'ro'],\n",
    "            ['f(x)', 'interpolation'], ['x', 'f(x)'])\n",
    "# plt.savefig('../../images/ch11/math_12.png');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {
    "uuid": "c3d9f85f-671f-4353-beab-fad9db9f8aa4"
   },
   "outputs": [],
   "source": [
    "ipo = spi.splrep(x, f(x), k=3)  \n",
    "iyd = spi.splev(xd, ipo)  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {
    "uuid": "8c67b514-160e-40e3-8f69-da81d7579b2d"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "False"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.allclose(f(xd), iyd)  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {
    "uuid": "ecc6c2fb-faa4-4149-b71e-05ac5cddeb79"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.1349319851436892e-08"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.mean((f(xd) - iyd) ** 2)  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {
    "uuid": "0c3e96f1-8732-4ce6-a6ed-bbaae732d950"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "create_plot([xd, xd], [f(xd), iyd], ['b', 'ro'],\n",
    "            ['f(x)', 'interpolation'], ['x', 'f(x)'])\n",
    "# plt.savefig('../../images/ch11/math_13.png');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Convex Optimization"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {
    "uuid": "a09a918e-760c-4e9c-95b8-fe3b568dacdb"
   },
   "outputs": [],
   "source": [
    "def fm(p):\n",
    "    x, y = p\n",
    "    return (np.sin(x) + 0.05 * x ** 2\n",
    "          + np.sin(y) + 0.05 * y ** 2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {
    "uuid": "1f4a147b-d9d2-42d5-8553-dd95d75d8251"
   },
   "outputs": [],
   "source": [
    "x = np.linspace(-10, 10, 50)\n",
    "y = np.linspace(-10, 10, 50)\n",
    "X, Y = np.meshgrid(x, y)\n",
    "Z = fm((X, Y))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {
    "uuid": "b3a1d3b7-25eb-4ac8-81ed-ad740fd1a297"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.colorbar.Colorbar at 0x7f866aa0fe10>"
      ]
     },
     "execution_count": 60,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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PHUlUjFMOfJjdqk99ref70WtXcBbmCfZlgcQ7l9r/tm2cmTSn3/tW3NIm5S99GvmGd/Vc5cYTj43ve9i2hVK6Mdl0N6mbB/dxYNislHogYxSpqRT4OghrkZSCKDL3p2EwjLA4JuwXFJNgkFbkzUwPUcv0iJBS4vuTG8dgDFaUy7Ikvu+wuXG794ZRRO6xi2z+8Zc63qpeuYJzepVgbYP573gLC/MRdlSChbPw2ibR+i3E1Utw7sHEQ9dXudCceSzLwnFis3qSST0IOvtsGGKmbeqfxGq8V1bKzEwWIZhigS8OyBUy2v15nN1khtEwwuKIM82uo706hkopSKXi1XaptL9J2HCVN/cz6rX02k9Kge97OI5F4cpl3IUZ+oWSytJ21/eyjz3MXKaCG+5B/Zm/u9n4zKKv/0lXYZFEFNUnj2bV0bpJvd4y3nFik/rCwmybZeOoB4keRJ2GadeZmBZhGJfQLhbLVKtxdsSwrpT+4zeuEMPRwgiLI8qggmIQq0OPvdmfoSGEIJVya03CAgqFzul5vBoYo4mSXpeXSrm4rkulUmVnp4y68jx+dZu8n0KXS133i9Zuk374QYovXG57Pf36R1ldUej8vn13NmH1HKy9hn7hKdjbRWRnhr6WOk2Teiw2LEsyPz/L3l4Rx7HxPJdsNoWU1hEPEj3e3UenXXJ7/4p90gW+DkZYSCMsDANjhMURY1gLRS+rw6D71vF9F89zqVaDPk3CxrNYTIpmD5KwNt5aoZ5XLyNUiP/Qw5SefrLnMVJnFii+0PL3o49w6h4HWcqjztyLvn6lfQer9pNRETzzRfj2d0/ykgCoVoPG6ha6TzqtQaL1QNGT+fA/7sKlf3DrOAW+LGv6k/54Ka2H/6wwHCxGWBwRRqlFETN6O/HamduahA2S6TGNqp3992sGfbYGku7tlYiipu9XKwU3XgIglZZ0t1fUtm9pTCYzGU7dn8ZS8VJSqKjzU711DTIzUNiFpz6Pfvv31Ro2TY9ek057kKiNUioxSPQ4+7mnPfRpVg2tH3/USXmQrBTXdRBC4Dj21KxaBxHHYTg5GGFxyFiWwPedhjl8WMatC5HN+kSR6pigp8fo1g4hRM01ICgWK8mxB3euQyV23zjlbdwz56jeuN59NOUyuTc+yu6Xv8HCO96ErZpxF2L9BswtwfZ6cwelsJZPERV2Y9fIlefgQnJjs2nTPUjUxnGsthVuFEW1fg8uYRhO9Ls+mBX/NI9+vJqQ7XelZLNptNZUq0EXV0oz7XnUrBQTY2EYBiMsDpF6+W3PG0dYDL8arTcJk1JSqVQolw+u5O4oQqi+GrMsSbFYaXMTdBz/+r54ifNnewoLAMdWuOfOMWvvdLwn5xZQrcICiNZvoxEINHzjc4cmLJKoB4mWW0JjpIwze1IpvxYkmkEI0THhjB4kenz7kMTHn3YdjukKo3rWzOCuFN32vQdBf6E5qrAYr9mh4bhihMUhcFi1KKSUpNPNJmGuax/53PR63EcURVQqQU9RAZ3Cwq3ugONA0H0/deMay29/C7KQkKK6cRNsG1qaVOndbeSZ+9C3XoGXn0VvryPmloa7sC5M415QShEEIa4bsb2dr51HNFa3cZBoel9mQtOkfhSYtsXiqLpCBjt+d2E0WIGvDFKKxMJuB3UNhpOFERYHSFItinEV/SD7x5kecSpmuVylUoknWcexx8ruGO1hM9j11it8BkHE7m4B17X7dkjUSsFrL7e9JsIKqYcuUnr2ma77WaunmLlnhfD5TmEhKiXE6fPoV1/adxW6flL48h/Bu/9y32s6StRN592DRB3S6dRAQaIHkbVxnIM3j1oMR/+slOZ3X3eltMZwDO9KMRaLuw0jLA6Ag6hFkUTcJKw9FXPf3hz0j77f88+2LdLp5MDMvqy9BtXO9NjUrN8ziDN9/3nswiaBZSOizhW6CMod04K+cQ0WlhDb6/DMl9Df8R5EdnbwsSZw2AvCUYNEpx2bczB1MqbLUY/h6Pfd+743kislblZohMXdhhEWU2SagqJJsjjolorZtucEsjsm9cBMqvCZdL6eY7pxJfF1u7CBtbhEtLGe8KZD1g8Q1RDr3gdQVy51bCI2b8PiKrRV89SQysWBnVEIX/00fM+f73eZx5J+QaKe52NZkuXl+Y6aCwcTEHx3M003RRhGKKVRSrO1tQsM5kqpVgOKxRKel9yTZxw2Ntb5jd/4IJcvv8hv/ua/A2B3d4cPfvDXOHPmLNevX+Mnf/KnWFhYnPi5DYNhhMUUGL4WxehFrvZPuK4bry6iKCKfL/UsEz2eG2a0NFetdZtLo9VNUypVe8RQDGBdufFy4stCQOq++9hLEBb+xUewdbxKs+3WupjtyGwOtb9M+M2r6OwcYm8bvvE59Le/G+Gne4/xhNAaJGrbFnNzOTY3d1sqifo4jtURJBqvbocLEp3mxGkahA1//EFcKV/5ypf5uZ/7O5w5c4YLFx7ioYce5qGHLvLww48wNzc31nieeuobvOtd382LLzYL0Pzrf/3rvPWtb+PP/tnv50//9I/59V//AP/gH/zjsc5jGB0jLCbIqLUoxitypRs/6lQqXh0UCuWxeg8Mdt7xLTH1wMxkN80IY+pisQDwZYk9IeOYiBayyznQewBYu+uwdArWb3Ue4PY1yM1BvqUMuFIwswB72xBU4Ik/hu94z9jXcRzRurOSKMSFlepZCUcxSPQg4ium7cY5CuJovyvlscfeyO///se4fv1VXnzxJS5ffoEPf/hDSCn5wAf+1Vjj+d7v/T6eeOKrba994Quf48d//CcAeMMb3sg/+Se/ONY5DONhhMUEcBxZKyAzqtl39CJX9aAq17UplapDFcXZbz0YntFKc1uWZHY20wjMHOSh2E/I6J0N2OtMF61jVYt4Fx6k8lJzlSPnFkjVREUde2mZMEFYCKWQi8uo/L7+IrdeQaeyiNIePPFZ9Fu/F+FO3vw7LocVp6BU7yBR1+0fJDrdifN4p7I2zzG9449addNxHO6//wIPPvjoFEbVztbWJul0BoB0OkM+v0sYhti2meIOA/Opj4llxe4HIaBcPrgiV80mYTZRFLG316/G5GSJH/jD7RNbVVyAiRfk6mWtqOMvzVJpSe5I3X8fsC9YLb9O4HiIoEIHt1+FdA6K+eZrYQinV+G1PSgV4KnPw1u/d6RrmC7TDPQZ7tjdAwXjmI16sGA9SDS+130qlerE244fjMXi+LtCjnrVzfn5BYrFArlcrvbfGSMqDhHzyY9Ie+qoHqus8zCxDkKIWqZHXFQrCCrY9mjnnoQ7YxCagZmSSiXAsuQIoqLPZ9QlvqIVr7KJyGTRhdhK4c+mQOfbthFhFfv8A0SXn+3YX0Qh8sy9qKvt+3D7VbTrIwBn+wZhUAHn6FktpsWkVuV190ip1B4kurAwgxCiLSthUkGi05/4p2sRgYNyhYy6CDiYjJB3vOOdPPPM06yunuKpp57kO77jnQdy3knxB87FQ1VuPxhcmugXZYTFkEynFkVnB8Qk4pgEh2q1mekRW0tGD8Acdd/B62fUO6XG9TPqFTSHP1+f9wewWAitSD30EMVvfB3hevi6kLidrat0jVBZew3hpdCVFgtRtYJ45E1k3BC7skH10hcoP/Y9fcdz8BztVWcSURShNRQKxYZ4sCzZiNvoDBKNYzYGDxKd7sR3EC6ooxBjcZB8/etf4+Mf/ygbG+t86EO/yY/8yI/xkz/5U3zwg7/Kq6++wo0br/FTP/Uzhz3MoRDOyUrJNcJiQHpleoy/8u/9o60XiwrDiHy+2GaWHOf3Ps1nRbNTapWdndYJfPK1M3SlDBsJAZdJ43I1RcC78ACS5FWY3NtCnL0P/drVjvdEUMG65yGCl56L/z7/IKm5DA4VtO1BpYLzytNUzz2Kmlsd4WpO1gNmEuyfnKNIEUWjBIl2li2ffjnvozUpj8JBBKAOw5vf/K28+c3f2vaa5/n8/M//b4c0ovGR9sn63Rth0YdBUkenVT0zXpG5PYtFjXPu8fZN/kxc1yaV8moiqLNT6ujdTbtbday9NdT8CmwmlOTeh1PZwTl3L+nVBWC363beTIbya8nvqfUbyDP34C0t4KkiREUAouwislJAoEk9/SkK7/rLMJSL7Ag9vYdg+gWQ+h9/2CDRunVj2pwEa8I4LdNNcazBsFLWYQ9hohhh0YVhalEM6srovX/zb8uKq08C3bt4tnA4v912y0M93VXrESpmDny+ZOT2LezTZwgHEBYA2XvP4lsVuvs7QGzewj5zL+GNax3v2atncM+dxrrzavvrO7cJZ1exd25j7a7hXn2K6v1vGmhMx53D6oXRi0GCRF3XwbIslpbm2ypJTipI9KQEh5pCZ9PFuEJOOKNVyxy/nK4QotaF0sWyLMrlCtVq/xVV/FA5PIvF/sZm/dJdp9HtUG7fwrIjQsuOq2D2wU3Jrm6QVkQu1/Gaff5B/DSIrduQnYtrWLSOpbyHljZChXgvfIHg9INoPzv4xRimTmuQqOe5pFIee3vFxC6grUGiQRAOnVJ+MJ1Zp3b42jnGCd40DIKVGift/+hhhEUNyxK1ug7D7zuJyTL2DTuUy1UKhcGLRR1UZkfCmXGcuGx4a2OzqZ2t23WqCJlfR6CQ5y6gXnkhYaN2rMUlhGPBvk6oHdtt3yJoLeU9v4yXFgitQUcox2P/7SIrBVi+F9auIcKA1Dcep/i294E8WabOg2Sak3P9nkrqAro/SHRmZpQg0ePvChnvHCdrJT4tLM8IixOFELGomJ1N7wsyHJxxJnffd/F9lyhStUyPYc998DEW9cDMMIzY3S0ONebRP6tky4zcXUOo+MFuz+WovtL/SFYmheVYvTwhUDubs7xMUBMW7tkzyKh5j8jddcKFM9ibN9pHun4dkVuE/Ab2xqvMfvOP0O/484S19uXDFDGbFNMUnwcR3De943efNPsFifp+PUhUdDTlqrsvp/3ZHH1hYRgEaZ0sAXZXCwursYicfuvy/TSbhEWUShUsyzrwyOthJ/nWwMz6w3b4MU82K0RuN+MqXCpUZxdhZ6PHDhLb1khdJVw4hdjsnU1ibd8imFuE7Cxe1Ck8ZXEHZXvIsLnSFVqhqiXwssjKHvra8yjxe9jveB+plN+lymQsNqYpAKZ7f013VT69Yw/3uQwbJApxA6+45Xg08Qn6oII3j3qBrOOOdE6WRfOuFBZJtSgOitis6qGUagQ5xp0CRzveNGIW9tPah6Q+Zs9zxiwHPhzdRJDcaRcG7rnzVHsJi8XTjfgKubiM7iMshNY4p89iyxBUZ2VVGZQJ504hN9pTSGSliPKzKDeFrJaQr3yTKha7tfoWzYZNrVUmI4QQpNN+W0nru51puxImESPVLUi0btHI5TKN73h/3MY411cXFjoMULu7qGIBVSyigwB7ZRV7eWWsa2s9x7AcxLPppGAsFseYabcx77X6aZ2ci8XyvkyPw/kB9vvhx8GkHpbVGZg5XtroKKNNPpjcac8EsR1FVVqgkh0dVksrZUsEBG4KUe1dDl36PsIB8pvJx9y+RbhwFntzn7go7xGlZ+Oy1GEFK79O+rnPUj7/RsL0HGEYtVWZdByb+fkZLMtqK2kdBCHBxm30nWuo3U1kYRtZ3EHbDiq7iMotEM6touZO9biK6a76jzPT0i1xRdCIalVRLMb3mG1bXYJE2zvADhokGty4ztYf/h7bn/xEXM8FsB96HeVnvwlRhMzmcO+/gHvhAbzXfwv+Y48hU8N14DWukOljOSbG4tgxTC2KUX9AzeyM9v1by1l3y5o4ar/ZZtlwuxZMmhSYOapLY3L7icIWImy3IkgdxsWtXn2JJKxMinqeqUQjTp+HV57veWYr7SN9H53fTBy5AKzd24Tzp7G3brbvW9whnF1BZWZw83dgbQ9n7SrB6gXK974JlWpmntTFZn53D1nawdpdw9m6gSztYu1tIwDhpdFBFQrboEL01i2ipXP4l79IuHCO8sV3ojLd2lJP70ab1j183OtA7E+V7Rckmk772Hbce6jVTRYEUVuQaPmbT1N4/KOQzyOlwLn/AtguUaWKVgr3gQeJNjaINtYpP/0k5aefhI/8J7As3AceIv22tyNnZrFXVmLLxtIywnGm8Bkdc4QoUngAACAASURBVNV5QAhjsTh+DGKlmISwaN1fSoHveziO1TdrYlIFtibxgOwsG97tnAdrsdi/n21beMX1xKRRZ2GO6qsJb0gL22rfw/JtQro//tTMIj5VKFcJTt2PdSu5dLjQGiu/Tji7gr1zJ97XTaEXT+OUtqGwQTC7irW3iYwC3Nsv4dy5gkrNoB0PZfsoP0P1qU1mNm+hLJcolUOHIextQaUIaHQtvVUjYPU8wrZxdjdBa5yNV7G/+P8R3vdGyve/BSUP6uc9/X4Y02LalsJBXC39g0Q9slkbKQXVcplbH/53FJ78OpWXLqMrZWQ2h1g+Q+WpJ2CfpUOkMzhnzyIch2hzk3BnG9Bsf/jfNrZxLzzA8s//feyV5Eqxoz5bhBDGFTIg0jYxFieSUSc8VQ2QrtPYXwjwfa/RJGxnp3/q6CTcA+PkswtB4wEWRZ1lw48S9a6ulmVRuf1KR7ongK0rVDOzUGhvoy6WTiHFPouSDgiWziLWk8tsisVVIBaFVlRuxEwkbqtVbKGYWUakM9jlPGJvvfG+s3MbbTkEs6uIKAQVIsJqbHXxwKrsgSWJvAwaC/vOK3Fq6z6imSWElFi1bBQtLaL5M1jbtxAqwnn5Cdztm9h/9kcIsfoWWBuX6WacTN+iN+0mZKMcPylItPzFP6HwqU8Q3ryB9H38c+ewcjOUrt+g8tw3E4+jiwWqL74AQuBefBRbCnSphPvwIwjXxX3wIeZ/5McQrtv9Cg7gO7jbMa6QY8ggE/fIVgOliAoldDaF5zk4jk0QNJuEDTjCsS0Wo64atdZks7HPtVAoD9i4aTwryzj75XIZKpUqhXwRf1+aZx0pwDp3nujSU+2vzy8mbz8/DwnCQls2ttX8PGQUEC2fg9de7DFKjczNgLTRlUKHJUREAU4tLkQ5KSIvg7V7B7u4g0rPobOzaOkgo2rcoj2sorwM2vHRwgLLwt683nZcoSLsrRsoL0Nku9iFLfTmTcqf/B2Cb//zOH4Kz3OxbQvXddsCB0cp+pR41VNMB512xsk0RfQkJuXgyovkf+uDqDAkunUDlELlQZx/gNJT3wCl8FaXcJZXkH6KMJ+ndOUKuiZKnHvuRYch1eebHXvT73gncz/6V3HOnu0zfhNfcRCIAwyEPwjuCmExCKNOlNL3iG7exj67TBSJkVb741TPjPcfftVYX/kLIahWp1/gqpVhH1T1NFetdUOwyfwaIuo+Zse3iPZNSla6GV/Rik2Vam4BuS84Uy+fw9rnbHFKW0RdLBxaSPTyPdiF+Dha2gTzp7F215EtY9XSIswsQFAGIVCzq8hyHu34cOsKzr7Pxyrtost7qNkVrPwdwsVzWDu3EWH79ctKAREGROk5rOI21tZN1Jd/j703/TmiTBrXdcjni41slLjoU7s/f9w25JPmYFbLRzOGQ2vN3r/9IOUv/imq3G75lGfuoXr1asP1Ee1sE+00q8DanovzwAWshUV0oYDaK8DSImg4/bd+htTbvn0gUTmusDCukMEwFosTyij9Pmw77umxc7VKtRIQRtFIq5/xXSGDi6L9gZmWJQmC4U3l4/ZHGYT9aa65XLoZw9LFWtHYlwBx+h70zXqvD4Ftd+lmKgRy5XRH1ofMZoFK5/aWQGVmEftcLWr1PE6hmeoqVIizG8dbaMdD2y6Rm0EGJey9DYRWUM4DEKbnsbZuJs6iWgjU3Cp2PnarODu3UY5HmFvG3mr/HERURQSCKDWDVdrF2bhO+qnH0W9/bzxGpahU9vvzJY4TZyukUh6Ok2lUmGwt+tRdbEzTqjB9i8VRDA5V1Qp7//IXKT1/qeM97biEWzvoamf6c2OboAq+T+lrX268Zi0scvaf/ktSZ87UUtz7B4kai8XBIOTJEmBGWNSILRaDbdvM9BCUShX06VV2nniGzBtfN91BdmHQ373nufh+PTCziNYa13XGqIQ5Gv2CTVvjKLpl0sitLq1HW7CXlgnqwmJ+qSO+om1bK6SankEW446nWkocki0iIigjZ+aIohBZjotmRbnFhqUicR8VonCxitvIoH31qSwHsbcZC40EovkzDYFSRwYVZLBGsHAOe/N6x3tKSCIvi1BhnCN/4zl0l4ZosdhQbVar/cGDuVwsNlpTIuvlrKdpVZh+E6+jd3y1vcHer/wjSq8ki2f7/ANUvvlMz2M4Dz/S5voQ6QyLP/8PiWbm2NsrNl7vFiRa/5611kZYHAAmePMYMsjvYhBXSH3Cs22LUqnaCKySnktpfYvsmCv4UR9y/cZeL8qVHJg5mhtmWj1K6uXCK5XOnikNQRIGyJ07XY7QxJFVAj8N5SJyYbnnthIQp++Bl+IgOL1wqmejMlEpIOaXUBsRslpGpNKI0k7X7ZXlIqKoQ1QARH4Ou5g8iSjbwypuJ74H4OzeJkiooSGCMtHSeSwb7LCEvv4sevleoHuQXtt5u1SYrLtRPK9ZzlqpePLxfa/W4Gu6waKTZdoZLcMdP7r6AuXf/L8ovZZc5E1kZ6i+1LvHjcjNEF672vYwWfipv4Nz730d2/b6nm3bwvPipoirq4sJZcvDPs+rk7UKnybGYnFCiRuQJfu5Wt0HlUqQ2CTMns1RfvUGYmVp5POPHoCZPMm3t1/fX5Sr974DnJVRHxz1c7Y+lOpxFEEQ9Q18ldu3u67u27ZDY527n+jyN7GyGfp9to4MCfwsoryHyM1BF4tFHatSIFo8TRhp3FJ3awVAlJppBG22ve5lYhdIF9TsEk4fEeXs3iGo9SzRQLRwFulIXFUmdBcgLMef1/Ofhwe/i5E67RHfo0mTUDabxrbrYiOFlFbb5NPaO2NYDqbOxNQOP9T4o1deovqb/4LK5l7yoCwLuXwavfFs53stOGfPtVkrvDe+Bf8tbx14zK3fcxQpUimP7e18w31SX6hYVr2SaNhWTfSgLBz//t//O27evMnc3ByvvnqNX/iFf4Dn+Qdy7kljLBYnlG4TbHtdh2LXH03urd/C7Q9/hPm/9INjnX+032T7JN/qSujXfv1wKmg2RVRSufC+5wz20NJqNB/rhZP1iKgHR/XeXgrQp+9FXHkWyxrsi7AqedTSPQSZLPb6q4gE8RL5uUZti8a1SItoZgnlpJC5eYSKEGE5npQtF41EK4Wz1bvkeB17d41g+TzSEjhRuVF51C5uEqTncYpbiOI2/q3nKJ95/UDHHAStde07C8jnYxP7/t4ZmUwKy7I6slGOgmXjYGIs+m+nSgWqv/VLRJWAoFjFWlwg/eCF2DVXrUC1HNc7KW6QfsujaC9DVI0It7YoXXml8eCwVk5RfaGl4JuUzP7oXx9z/PGx699bqSXburWSqO+nsW2LX/7lX+by5cs8+ODDPPjgRR566CIrK6sTjcna2Fjnt3/7Q/zBH3wSKSV/7+/9HT772U/z7nf/uYmd4yA5DsGbFy9e/LvAfcA68BDwP166dCkx994Iixr73Qmu65BKxU3CBsv0EKhKBVWpIr3BzM3J5x/dYtGsoWFTLidbVhL25qBNllrXxY/fM46i286ysI6aP4W1MUCcha5in38IWw42ibmOorp4BpfBxhPmFrErcQBmtHIPOoywN2+0CQyNiAM3s3NoL4UQAqtaQEgbp7je/ulHAXbNXRLMrKAXV4iUwF5vj6PYj0rNYLsyLpy171Ktyh7a9hBhBe/OZYLZ00SZhYGubxD2C+Kk3hlC0JiAHKe9Udf+INH2Yx9vE/H+yptJaK2p/vr/jggDlJti9vUrsLsFr7VXjxWnzsP2c+i12MJl1f55D5+B+RWiAEIklVIBlY/vyfT3fB/OPfeOMf7ewiupkuj73vdDPPPM0zz//PP85//8H3nhhefRWvH+9/9tfuAH3jvyWFrxfR/HcSgUCuRyOUqlEvfff2Eixz4Mjnq66cWLF08BvwAsXbp0SV28ePEjwA8D/0/S9kZY1KhP7ElNwgbdf/HPvIO1P/gUyz/8nlFGMPJDVGvdaOPcz7LSue+oFovRxyulIJNJJcZR9DkrFLcRUYBKZRjUeOjedx+UtgYbGxpx7wXId7otEkfkZaASB3xaYXwtemEZJW20tFGWh13JI10LSQTVvca+yva6XoOWVlxgS4VIIDx9P2J3C6vQGW+h/Awim43rbHhZdLXUJmxkFKAyC4iwgkCTvvYE+Uf+DIiDbSKX1Kir1bwel7O22nz58b5HL2tjksevfvjX0NsbOEtLsL4OO51uNQ3ojS4usWIBilew5pewttbx5ixYPYWYmcf7iz8y1vilHP7zmZ2d453v/E7e9a7vRkoHrTUbG+v4fmqssbSSyWR5//t/mn/0j36BxcUllpdXOHv2nokd/6CR9tEWFkARqAIzwDaQBZKrskFi4cITxyC/Cykltm3h+y7FYnkoUVE7C9mLF9j7etfPeuwxJlEPpJNSkM+X4iyVoQ52cBYL13WYnc0AcTGucrl7ulwSWoPMrwEgUKjUzGA7zi6grcE1tM7OEHnZvtspy8VqEQp1BCBViBWWkSpsa6neOIcGq0ewZ5RZQKjmJGxX8siUT5hrL/KlEajZRaSOzRRWZY8w1xnnIwub6Jnlxjbe2st9r+8giE3rZXZ399jY2Ob27Q12dvYIgqCWzu3jug6Li3PMzmZJp30cx56YJeOwq0oGf/px9EtPkz292NH3phWxeg96u0fXXvYVgKuUkSunsebGs0xNooCYEIKlpWWy2f6/qUF58cVL/M7v/Db/4l98gL//93+R2dk5PvSh35jY8Q8aIeWh/uvHpUuXdoG/C/yHixcvfgi4DnSNIr4rhEUvpJRkMilSKRelNPl8cSTfb/3h5J09ReHZ3lHbyfsPZwGwLEkul65ZKQKCIBqpguK0sjtasW2LXC6N59ktgm20KqHUhAWAmu2d6VEncH3CuTODnUNIsATBwum+20azyz2DSJXldBUPoZ9LFBx1hO68B4UKkb5L1NJkLFo4jR21H8cu7SQLo+JOo3+Id/tSz4lsGCa96g/DkFKpwu5ugXy+WCuNn6daDbAsi1wuw/LyAktLdbGRqqVNj3IjH16fE3XtBfiT3yezPIdWELSkge5Hyz72OWmhbrW7Bu23fc/YYzyqDcjW1tbI5Waw7fh+XlxcotqjrsdRR9rWof7rx8WLF99ELCx+8NKlS3+NOM7iH3bb/q51hQghSKVcHCcuFFUqhY3S1qNQFwZLP/TfcP0D/4YL//R/HXL/wSb49pTXODDTdR3sEU1p4zZA68Ug9SiGQe1tIqLmw0PbEi1kz8ldWw4RApWewem94IvPkZ5DIGJxMXcaZ7t7xkZSoGbbsew0ViV5shBR988i8rJYtcJZ+4ndGmkiHSEr5bhGxb5hCK1Adn42IqwSZRaRhQ1kFODfeo7SuTf2vIajQt2X31qwLClwUCndFq/RL0th0ODKUeg1Kev1m+j/+Bv4OR+0JlJAmHxPaD+Nun6197nO3Ye+1ozJEHMLWBe/ZdShN49zRAtkvf3t7+ALX/gcv/qrv0Iul+Pll1/ip3/65w57WKNz9GOJzgKbly5dqt+kN4GuwTt3nbAQIi4UVa+VUO/gGQc/jt9h1F1donp7nWivUEtxHPgIPc/fGpjZmfJ68AGY0DuTJZVycd3e9SiGJdoXwCjQqLlTWFvdq3Cq3CIIgRYQZRex9vqYk3NNa4DKzqD3NhFJroxUDivoscLUOtFNAqCk3bM2hfIyWMXu1gwZVlHZWYKZZdywkLiNVS0SZBdxWiw8AFZxk8hJYwVF3PWrVJYuoPxc4jGOAr0m/uQW5Faj1kacBmu1BZPuFxvxbTidibPbpKwLecIPfwDfbf54AtV91SiWTsHuC73PFYVtV2F/23dNJCDwqAoLy7L4uZ/7+cMexsQ4BummHwN+4OLFi79MHGPxGPAz3Ta+a4SF1uD7Dr7vJjYJG9cl0Lr/wru/i7Xf/UNO/bW/MNT+3cSB57WOuzMwc5yx96rfMcDe7Dclt2bT7O4W0CqKq0pGAdr20NkRfb5BCZVQxluls1g94jKj9Gzj/8OZpb7CooJs+xailfPYNxIe6rkF6BUj4edwCskDU04au5wsOgBk2D+gVagANXcKtVno6s+0S7so22tzuQit0Y4LQRGBJnXjGQoX3tH3fD3HMvU4hSEKTEVxSep2sSEbYiOTSeE4dkNs1AO2tQ4m3oys2+eiPvJb+C5QO5+yHNSt7sHCup+lb2YedeNa828hsL/tu0YYcSf1AmjDMk1L6EnkqAuLS5cuRcBPDbr9XSMsZmfTRJEmny9NpJvjflp/SAs/+D08+5f+Fqt/9b8f+MeVVFK8NUOl17gP60fcarFo1qPQzTiKoIz74uexaqvmKLsIro+67w2IIdMd5eY1kieYCOVnkV0matUSiR7ZLrgp6NL2XAvZoe0iKSC7hN3S/hziSnm9H7c9vo9e9TdSWaxqd0tInTCziBWVCebP4nUpby50RJSaQ+7ti8EobhP6M9jlXZzd29i7twlnVvueszvTW9VOQrREkSKKqm3BwpYlG0W94mZs2UbmSqsbZZxnRdJqX9+8ip2/02geBhCk5oFkYaEdF3Xz1Z7nkYsrqN2miJX3X0TOJXfyHZajarE4aZjKm8eUfL40UD75JH5Idi6Ld+4U+a88xczbBvNht1oOLEvWKmaKrhUzJ0UsDka9qTVCSDIZpzOOoriD//xnEUFzEpd7m+j0DPqbn0GcfhhWLg5magkqyN3kQlFCCNTcCvJWp7DQ0moEK8YbQzB7CmftSuKxovRc4mcRzi6CCrFr7gttOVDsbq1Aa+wu4kAjemaDiPQseoBy5cpxkDpCqIDQz2F3icmwStuJ7wut0ECYW0FWdkGvjOnnndbkM53gyrrYANje3q3VVmlaNuLU1/jeaRUaw3R+TXqWyD/5r8igXehF291NbmLlLFx5sed5dLn9XrMf+9aBxjcIRlgcDOKIWyyG5a4RFkr1bzI2XvXLdlb+ynu5/aHfHUJYxOfOZPy2wMzB9h2vBsao80lczjmhHoVWuNe+Dvt6bQg0yvHjDpw3X8DZ2yI4/61g9y4oJrZeRfT4UrRloYXo2EZnF+Jymi2EqQw2okuFzOR0OCEgnF9FqAirnEfNLiGDZKsH1GMkksWD8rNYu2uJ78WD6N++PvKyjfRSgSbKzCHLe8iEaxKAkJ0/c6FCyisPIiTIqIIs76BScx3bHTYHkQ5aP373zq/NNvOOYw3c+bXjN/nCE8g77daHyM+hr77Sd2zdEJks+na7xcp6/Vt67zQEowoLIQTiAOukHHdOmtvorhEWg8QhjFP9snV/rTWz3/k2XvnF/5tgYxtnsfcDWwhwHKuRoTJc0aiDSRltpR5HAVAolDosKtady8jSNlFmHnu73dIgirsg4gFb+TXUjW8SrT4E3epG5Ncg7D3ZCqFRsytY2+3mZDHT6W7RQhDNrmLvdFpAtON2dWAIAcHiGVi/HguhXsJC2F0LX1k96mkoy0EmFMDaT5SaRbSU15RhmWDhHN5mssncquRRuWVkfg1lu1RnT6NtBywbrUIEYO/dpurPjnQjTXfyP9wHbrLYSO782u5Gib+fxqQcBthf/njHkyXsUS9FS4m61bviqnP6HqqXn2uO7cx55Pxo/YqSMBaLg+Gox1gMi5GULYwbq9A6wUvbZvkvvIc7v/Nfe+7jeQ4zM80H07BFo2pnZtQH8DDXXK9H4bp21wJiolLAvnkJABmUOx6kMihBS0ClVdzGeu0pxPaNztiDwiZsXkOHpXaXRgIq3Vksq+IkNyQKc0mCozO+Yj9CQHXpXLxtD5I6mDbGubeNcnzCzALh3GnUzBLUxilnFvvO0BoBIuFzjyqEfveCYSIoEy6co7J4LzhOnAWlQpQTp1jLKMAq9m6k1p3p1YIYpCT2OMcehXpH0EKhxPZ2nrW1LdbWtigUSigVd3mdn59hfn4Gx7HJ5TKkvv4x9Hbn5xvt7nYf3/JZKHcXsAB6X4qqNUE3CIwevGkYEikP99+EuWssFoMwvrBot3gs/4X38Oxf/hnOvP/HOlK/9gdmShl3UB3tvNO1WAxTj8K+8c1GcScRlFBJKZ5Ry2q7nEd5aayNK+itV1Ezp+JiQJUCVArxXK81KjWHLLQHULYhNHhpqNWN0NJCWU7ipsqyOlJPo9TsQN+9dtOUUjM42QXs7VtY1fZ0T2W5WJXma1pIIn+G0M8RuT4yLHeeJ7uAVhosl1RYhVJyvATEWS5Jbpy6S8QuJ09U4ewyUWYuthi1IMMyuuYasgtrRKn5qTxojiaTW40ndX5NpTx83yN69RL6ynOd+3gp9LXrIC2s8w/gzWWwdIhQEZKIaHYFtZwl0A5ROSDc2UHdfq35+3Fcgteuth3TnqAbZFxOmnl/mkjrZFksjLBoYfyU032NzE6fJvP6B9j+zBeZ/zPfAcSBmamUhxDtgZlCWGPGSUxn31TKw3WdLvUo2h8eolJAbu9LCbUTbrH8BmRmoZYGKVQcSChUiLV9ndDNtpWzhv7rYSEgmlvFuh0HZqrcUkd8RSvB7EqbsFD+YDVHItsHHRIISXXuNFYUYAWVuDtpFKBsh8jLEjkeynLQUjY+Iy0dRJRcn0JIQWRZFOdOY6XmcbdfS+zeamVnCYPkY8iwRJBb7qhdUZk7E2fEBBUQEtlaNEurRl0LoUKs4jpRdmWgz6JxjCnOH9M0xR9E/EZYDZBPPE51IyHNeXaF9BtWcWWADIoQtIs+XdzFDgq4ED+pF23U0gWqdpZqJQIkweXn0cRiRiyuIE9Prl+GcYMcHCZ48wQzibTN/buv/sV3c+s//B6L3/dOfN/DcSxKpWrbyqZ29rHOOw5Jl9ysR9FZ86NJ+2vW2ksd3gRR3EE7HqJlMhRotJtqCAtZ2CTMzDdW4rLm+287TlhBp2YQpe6mY+U4jdiGKNs7rkXZNlFmHqtWa0I7Xs/t68RBorUxCYGyXVRr8Km02+pQtH4evdq8K8ttWHoiz6e0cgF3d62RiVKnGgQ9/Zfa9VCIRiBnmJ4n8msVZVWEctPISnsGjQxKaGEhdIRdWCdKL0Af11PHeY/h/DNOPNWgx9ef/y+o3W30frfh8lmchRms9esd3WgBSGeRO53ZIlJH+MEOvgROnQd5hki6RJZHdP9jkx//cfxijyEm3fSYMsjvYxKukP2O+ty73sH1D/w27vYGauUUOzvJ/vfDq0XRPuZ6PQqtdd9GbG0WnijA2rjWsU1sou8M4qSwg65VGxUqQkgHVBxfIip7KGF3CB7tpnsKC4FC5ZaQ+XWU1788ezi3ilXYijtHStk3SkUBqO5uIK01MkqOkdFaY3WxVgC1QlYt94YQVGZW4tTVWnpq5GWR9E51FGEFvXwvrL0CCMKZJVonTxFWUNJGtlyHQBPZXmy10Ap7b41wpn+vlJazDrHtcAjRVvIhbitfWMPJr2MXNtGWjbYctOUSzJ4myK0OYUKZXjlvAG5fQ669QmV3Xyr0vQ+SSltEO92zgyJ/JlFYtLEbx2xYqoqlqlTuudDn7hiOUTqbNjlZE+W0EcYVcrKZpCvE8xz82Qyr7/0uXvn3H2H1b/71HvuOcO4wQNx8GaQkLC8iUgtDPyjr5x2tr0dTlFgbr3S4L+rUgzjbVu/VImpmBVGJ4wlkZQ/lxCt/oUJEKgv7giBVpYSQdtfzAKjcPKKURw3wQ40sG5WaRWs10GevnHTv/iDSQURdAjelk1gavBdCQGV2BaEVVjlP5GcHelxHQQUsF5VdRO0br0Aj/UxHHQ4ZFFHSQao4iDNKL6Dtwaw4MdOsY6EQQQlv8wqyUozdOWEVbTmx+6aWoeMU1om8K5QXLxDm+tflmGZgKFpjfe1jaK3RpZZaLg89RtqqEHgZRNC9XonuV5hrZqEhLACwbLz7LhJqQRiGExFMk+hsahiQExbXZIRFC7EwGP0Lrk/SjmPVAjPjVf/se7+fl37u/2Tlx/8SIp3syx/WYiGuv4D8yh+iM7NYWzeoAPLe1xG99QfAGSYIND5vLpemXN7fg6TPnq1iqEfvi65BnKo9iDPyTiFUzV8cBZ1TlVaQXYDdHg9kqYnmTw2m0oQgmD+N7BEs2TZcx+9psUDKZLN27VxdjwttzdXadxOUZ0/ha4W2rMSupx376Ihg7jSRbScKEVUpIGy3rbupAITjQiWIAznztwjmz/c9VzzG6blChAB2b+OtXUMGZezSdsc1hf4MqAi7WsCq7JG69U2q5S2qC/f3EUfTW1U7L3wRGZaJqgE6iO9p65FvIUX8+1JadnVpaa2Ruz0ClYlrrlitwuLUfTi+T8q2sW0bpaK23ihhGA0toowr5OAwFosTzCTcEZ7nAppisdIIzLRPncG97xzFz32GzPf/4NjjlE9+Gvn0n8R/VIpx/YWwirz2LGLrFuF3/kXI9S/p21qPIqkHycCUd9E96jMAiUGcsrCJ9nMNMSFV1BATolpAJQRxKqW71oiAeKoI5s8AgxUXi2wbnZ5B6P7bx9kTPc7dI4ZC9hIklt9TMAgpKM+fw64mNxxLInTTaCGwVLJgiSwXe3/b9EoB4aXRlSJWJY9nx4Gd9doMB46K0NefReY3sfc2u3axrWfChP5MnI5rWTjFTazKHuWVR1FespifmsWiUiZ18/l4TIU4S8k6f6EhKgAodhezOreI2OreOwToKKQWrN5Pabd5f9h2XBfHtuNaG7HYUCN0fh3t8zEZIcNx0mIsTpb9pQeDxViM5goRQpBO+3ieg1KK3d1iR9Go1R/979j45BfR0XjlucULX2uKCkCEAWpmufl3fhPryU9Dj7bc++tRwGgP2LoQE/l1RFgmSvWoo1Da6QiQFFqj3WYshCxsxRMDsUBw3E7Liw7KRL2KCgG7qeWu73cOTFDI9I8nUIi+8RXdrA5a655uEGUnp8W2ErlpirnB4x7KboaKN9v1fRGWUQmr+ShsirvwzlVs22JmJsvq6iKLi3PMzGRJpeLqsC1HG3hcjbQqigAAIABJREFUgyJKu3hrL8LeJqJSQLlpwtQsQWaB0O0UCpHto1wfIVQjzVhGVVK3nu5an2NaK/LMM48jakXdwnwBOb+A5zcftUpYiJ3uFgnlpbq+B3EKs9xu3z8680Db32EYUSpVyOcLbG7ucOfOBtvbu1QqVaSUZLNplpfnWVqaZ24uRyaTwnWd9iwvY7E4OCzrcP9NGGOxaGEUi4XvN1uwF4sVbDtZq6Vf9yhKeoTf/BrOG97W5fy9f8zitReQX/lo5+uF9oBGcesK9otfJHzkXW2vjxZH0RutFKIYuzhUdhGrS3Cl0MlBnKK02xLEGSIsB2oTtC7tokkO4qTSrenYLGXhknHScQpfv/FbDrtWFtebxa107+Gh3D7xFZaD6NaVtG98Rf+Hd2R5VKSDm1rALfUuZBW6WZSwQCtCO4UddhZZEoCSVsfKQkaVOJYkKEK1SOHOdfKpeYBGaetmLw2LMAyRUhJFNlEUjd3Xxtl6BWfvTq0bro+oBa4K9q3Q0/PIsIKolghzy8iw1KgpYlX3CL0Z7MouQiv8O89TWXyAMDdOo7XBsNeuYtXucVUrXuWvLrcF3UZeFqG7WyREpbc7Us0tY7VYNHQqi57vf22928xbHZ1f65yUIllHueOqcYWcYIa58Trag2uN69r0Wr3lvutd5D/7GRa6Cgvd3V+9t4X14lcS3xR7W7B8FmolrUUUwMZNrNsvEa3GK5m4HoWdGEcxao8UrTV6b6PhAtBhNZ6surgEkoI4ZbVIlFtGVGOhYAclQln7kUXJQZw6qKD21WOoU/biNNOyM0N6AGGh7NhisuWtsFLd6+qSULbXO76iV2xO3/iK/v1BAhF/Jnv+PHPVva7ZJwBVr2k5qjjZRGEB8Yq+XsOibbhRtfE9ydIukT/X1h+jFcexmZnJYts2s7MulhWLjfbGXQOIDRXi33keuxbMGzkZnB6VQO1KHiUtqvNnsEs7baJPAHZll9DLYVXyCMDbeAmEIGyp0THxFbnWpF78UqNnTRRo/PP3IvcF3qgw6h5fIS1Ej2wRoFGptU50+sKoI25pM998rd5mPpXysSyLpaX5htgIw2jAzq9HbwIXQrC3t0ehsFezMmfIZrtbPw+S/QUUjztGWLQwiLCwbYt0uhmY2ZqO2c+VMv/97+LGZx5n9voVrHP3J40Aksojqwj7S/8VsXUblZ7pqJ4IgGxXvHp7HefS57FW7iU1N1erR9EtjqLLeQdA7TRXTkJHRLOnkN3aeAclVGYBq9A+YbR9ZoVt9OxqI7ZCRGHHqIRW6PQ8FNqDQTWwZ+fiw2iXVJ8MEoCqFbsDImFTSK+QLdxM3G6c+Ipe72F5XWMHGueWNqomXLSQFLKnyO5cSxyPlhYVq+lC0loROFmcINnCA6qt7kU83jCOrbBcCnYWq1rC65K+W59gCoUS1WqAEDT6aLiuQyaTQkqro0Noq9gQ5V1Say8ga7E2StjYpd49U5SQhOk57EqeyMvWCny1f852JU/kZpHVvVhcrF9GC4soE8cfTTro1L32JLIl28bKppFJojHfPY1U5RaQ6ze6vg8gyu3fpTr9QJctR6Pe+dW27Ubp8nqb+bq1KrZstHd+HbfN/KBcu3aVxx//OJ7n8Y1vPMFP/MT/xOte17uGx0svXeaTn/w4pVKRUinudD03N8+DDz7Et33b25mbmz9ca4axWBxf+k38vd6vV8yUUtTcCJ2TRT9hIm0b59w5yp/5AzI/9r8MfH7r6c8gt2ouhPklSBAWeu01SKUR1Xh1Kva20AtL2C99lb2L7xyoHsWwD1kVVNF77SJBdymj3SAhY0XmN1CpDKIWFyJazK6iupcYxJnUr0P5M4SidksLQeDN4pYSKh62UKEZZ7BrzZJydjpW8APVr+gSJBnXr+jRO8RykT3eh1q1zxaqlkc1vYRX7PTTB/5ch/Wkaqe6CguhQpSbQVab74dOhpI3QyAcQBOFAZEVYHWJBWm957Wmw7IhhGgEE3qeQzabRkpJGIaUbl5B3n6h3c0krb5iK8wsYgU110dQRFkeQoQdlhyruhfX/6jE4sJfe4GyeIQoPc+oYjqRKMS/9nTjT5XKIkudwbaR5fUsTa/7dPrVjo/Ybb+nx7FY9CJON42/h7rY6NX5NZMR/PAP/xBLS0s88MDDPPzwo1y8+Ahnzpyd2KQdRRG/+qu/wj//57+ClJL3vOe/xeozKT/55Nf59Kf/CKUiZmfnWFk5RRSFbG5u8pGP/Cf+y3/5j7z//X+bxx77lsNzlxxRF82o3FXCoh9JN5UQcVxC94qZvfffz9x7f4CdX/2n+N//Gtbq2f7nv/481otfbfwt9zZRUiL2rwxUBDNLsN7scKkqVcSrz6NWH+6TJTKaxULnO022IiwTpWe7tg0XpR207bXHHGiFdjKIKN7HKm4R1npiCJIrcRKU4yqS1aYIKHvzbZvskaKz3VjLaaVFRVtNq60QbPmnWAyutE102k5Nr37FAM+T0OqcbPa8WZzyTmOVX6dqdwb+aa0IU3NdrQBCVeOYDGlT8OcJZCwgWl0F1WoJ37K73t+9XAp1M3qH2Cis4a5dbndjuCnsvd6FocLUbENU1JFRBS1tIifVqGtRx6rstbhFNN7mFUq2i0h5E7NY+K88gajUAqEtGzWziCx1irnISfW2fJV7u+/UzCLWRtMiqOaWITUdc34/V1FS59df+qV/yYsvvsBzzz3PJz7xUX7t136FcrnMv/k3H+bUqWGKriXz3HPPorXmd3/3P1CplJmZmeV97/uhrttHUQQIvu/73s1jj70hcZurV6/wqU89Tjab5b77kizJ00f0y6o7Zpysq5kwrYGZ3SpmtjJIVol333nkzByVj/2/pP/qz/bcX2zfxt4XrCkqJVg+B7c7q1yyu9kWw6DvvIo+dQ7n8peovvkHxhp34n5d6kmo9EJ3YaEVYnYJNtrdJaLcTL8TUdAWxCmqBRSyY1JTbrYhLLS02LXbs1IiYRHVJpTEcdrpjguvSo/d7Flm9q43Pkfl+NCrfsSI9StgwPiKpARbISlnlknnm2ZzLayGKNhPVbhYtWZjHYfSikpqkZJ028arteL/Z+/Ng27LzvK+3xr2cMZvvmPf2923u/laAxIt1BIyQhKlSohBBMfYJEAFYpLCZWKncCpl8k8SQgF2KnEgtiuugthQAeOCWGAbYwmZUYhRArXG1u2Weu47fvOZ9rTWyh/7fGfce59zh+571fc+VV9Jfc+ezj57r/Ws933e55VSYa0ZNtkqT4ncKMTRFfy9MYEzXo00XEHikH4TKQVCSKQzsHdplOawCJwodkkVNgOpMTpEzQhpddwhC9oILJny0YevQC3E6fJKpmUh+wd4114Y/bfbOAklEUKXpqXEwikPscC/YjZk7k69dhPhzYg219bWefLJd/Pud78XOUzPdrvd26ZluHr1Mp///Of40R/9SZrNJj/2Y/8Tnufxrd/67YXbSyl5+9u/DsgJhOd5nD37AJCTDuccDz30MN/3fT9AvEA0+5rifrnpGxvO5Y6ZKysNpJR0Or2lW5kvG0bz3/N+ks/9OebqrBZhghbEffQf/WrhxFMaJu4d4lZPTm1npI86uIK8/mLVld94+C8dQFQcXncmxsry8KSNx6syJySmsY4NmmSNzdG/y4lthEkR/nwLdGcS7PC64+apfNU9g4EqH9BSVdxWvadadBtnRlOwWyCsqgrbV3022R+kapuyNu0DXcd444k+C5qlRMZaQ9Yojlol/gpd1SjsD2JtvuID8pRItpgILYLoXic4fAWBI66vM2idJvUbuQNq0s+jUfEAE/VI44i0dYJs7UxOKFZPICus0fOUmcOq6VJaq/KmcGnQziNhzmKufmXqWbxZhNe+hOzmRNo2VhCNJrJTIjw9Khek2tbafCRyBmLG/8K8hsTidolbb6dAsl5v8OCDD42O+ba3vZ1Pf/rPS7cXQgyjFvBHf/QJ/vk//xmef/45Dg4OUEqhh/46WmsajTsn5BRK3dG/2437xGICWiuEyCs+ut0B/X50g4x9vldIEVr/0X+CVTXiX/q/IBmz5JEvxOE1vD/9N6UmOvLoOq5VEuSfvd69q1gH3oufKRVR3MzYIbrlKyvhLGalPOwpkj60NrBeje7Zt3K0dYHO+jl6Gw9yePqtZI0N5OAQNzHRFQkghTW42hpOSPa94vsxwEd4xQQiluWujB29Qn/ob1Flr1zlXwEgq/wrClIcszCqwjlSCHr1sWdH6lV3aE1sLoycROY36ahc8GqnJJyTpxk/03E8wM54sdyIPkd0r6H71xE2Y9A6lZOFY7dVoYrfHpths5SofYpoiSCrtBlIiZUeTgjS+jqpX8u/YTbAeuOmbOmlZ0bN8G4G3t4LqL3LgMv7lmydwjiBjOf1FZkXVrq8upJo0+jzsI6cTBMJgTmxnDvqzeBmiUX+vLw2K/C3vOWtHB4ejsjClStXOHfufOU+crgweOyxr2Fzc4tPfOL3+cxn/oIrV64QRXcwSjEJqe7s323GPZUKKQv5Symp1wOklFhr6fejSrHjjR5/FkIIgre/k/TTf4D75Z9C/OXvg9Y61vQRl76C9xe/nSvz104i9q8UHkOtrmOLVkV7l3HNNiLKBzYx6GA3TqE7O4j9V3Dr822VZ9ufLwMxa889e8wFOUNXb3O09uBUNMClEamuEa8/TKu2gjfhNCniLs5vTNmAQ54CSRonC6MVx4iDNfx0ptpDKiKrK8e/Q72Kt+YhqioUpC5the6EQtgJ4jibiljinpsFYthU+aThKjo6JJELhH/OEYer1AY7o+s7Uiuj63DOIaUHM7qNyZQIOKKoR1hrjELdy+pzRO86MjpCWEfc2JoS5Drn0GU+IMfbeCHWGeLGFkGvuiRTmATRWCWVHi6Np55vmfaxXg2ZDsBmeAcvka2cw5UQ0FJkKf7hJejlkTtz+mGUgCwpKVmWwQJ9RVnlznD/5jpqQoMhT5yFBWZat4K70Xmz3V7hb/2tv8M/+kf/kNXVNQ4O9vkbf+O/Wepa3va2t/Pkk+8G4MMf/hV+4Rf+Hk8++W4+9KHvGKVH7hi+CspNt7e3t4HvBgbA+4EfvXjx4p8VbXtPEYtZ5MJMH8/TRFFCHKe0WrXXRRUcfMtfJX3qE0Qvvkjjd34J5UnccHAeaQmrHrb9qzjtjRz+jiGcwzVWR8QCwEV9kKAvPUu6drbAc+HGBg+bDBAmrh4kswjXWEP05oV4Tkg6zZNYa+dSBZ4UJNbRqa3j+S0a/atIk+elhfZxybQwzxnDfr1aFHZoPLaUP9JsAFCRNpjEDqvgt9jgAJHMrzaFUnP6CofA6BqxauC8NTLhkaBxSDxSfJfg2RjPLl4pp0u8or1wnYazC1M2AMY5jApQJiYKVufSLMY6lNRzVTDWmnlyEU6SiwXo7iCSzlCI6uZTQMofeZmUwQqJcAYnIGqdwu9cKQ25WumROIVAIaSai3jJdIAIm7ioi7AZev8FTPsMNlxecxFcfwayFBkPyNpbKC+/GtEvSRFW6St0MFftMYeZ31ed+5qlr/VmcLc6b77//d/M+9//zUtvfxwJ/sQn/oBO5whjDC+++Dyep9nb2+UXfuHnOHv2HN/xHX+VdvvWNTc3hbu83HR7e1sB/yfw7RcvXrTb29v/LxV9E+5ZYnEszEySdGhwlf/7rb5Hxw/xohdSb2zhn3+Y5MXnCPf3EBe2kTPpBXFwDVdrIYrCp1kCm2fhygvznx3sTK+Ody9hTp1D7b1CdnAZtzZbjXJj4s006mEbmwTd6lVjVl/FKyAW8fp5YhTaC2C2/0UWg/DyclHlcbD6KCvdV3JFf9LPf5/jFbZQXKs9mA/KVSWbQhCHqwS9sdh0wHKdO42VxFbT5yR1r82q20e5DOkMzhq0UvlKWockwqfvfLomBCGoqQwzk5pK8UmFj5BNMidZ0Yc04p1CLYaVGrdMVEMqus1T1QZeE4j9NmFySF8Ur3atzcnt7JmtNQipcNaAc8RRj6CkD8ckXH8flRwReSuEWa9wcpULtCZG+aOUSX5QQ9I+jX90ZS6B44QiDXMtBSYZalniOUM1F3VR9Tamf5Q3Xjt6FUjJahtzGcVZ6MPL6OQIBoOcnK1vAA7nQJUIMI+Jg904g9zYQiqGlU+OLGyju/tkRuCSBNfrIPavIdIx+RTd6ciZOvdY9UXeIt4ojpvWWpRSfPSj/45r167y0EMXePLJd/N3/+7fGy0if/qn/w9effVl2u233JmLvIXml68TniQfEv7O9vZ2HdgFfrZs43uOWPi+plYLyDJDp9Obe3FutY75RjwhvPd8kPTF54iu79M4Oz8xChyuvQ4ledmyMkYR9XBbDyCG1sLCOaz0UWkXde0FspVTM3m15b+zsxYT93AyWDg1FzlxWr9Bp5brIYy1KGYmMGvQfkg21DUIDJfCh9jw96kNrqOCOiYZ4KRit/YgfUJkBgHV5KhjQwLljZo3DcRyxCKz44P2XY0+tfGsKyy+MRgpYXLOGu6S39MSe3YpwQoOxSrdsMW62cFPpitprF4+NH9g26yyX3q+qeM6SyfYYp465HCAkB7Ozq+w3ZBcWGMwMmAwMNjdI3TJebP+IX60T+Sv4JCFwkuHQKULbKy92lyKBpsNycWlqchFWltl8j4c24PbLJojF6Z/hPNqiDTK9zm6Ruh5BKtbOOVPmT8dLxbU0TX8gxfzBNCgT3biQbTIP7NOoAsE15nfwG2uoVp1fGGZfmDyZ0UJi9KAVlBfxW6uYpzCRCmu30XsTdh4S4U8ewEOb118Woa7MRVyMzjWWDzxxNfzzne+i6/5mseBfKx3zhFFETs71wmC5caE1wR3ecQCeBB4D/DdFy9ePNze3v5FIAF+vmjje4pY5FEKNeeYOYlbJxauckKZhPeO96E++v+RHB5Qv/oK9sw5ZDRNImRnF1sQyoXc08KsbiEOCiIHs83Odi9j2y3UwRXM/iu4jbHo60bGjizuAg5rM7KgiS7p2QEUOnH218+P2LlzFrxaXmEy+b1sCsMSS2dSPBWwK9ahscaKl3HkaSLnczwxWgfS83EVIkonBLG/SjC4jlPeUikGAOPKnwUlocycWQpHVqHTkVKOhLZGKK7rk6wLTS0eh8PNAs3EGIK+8al5DQJbnU7IN1cc2hZ10SslY9Y6pPBwbp5cWCewssaxR9xRNycFvpZoJXBuuEo0PerxPlGwRoakboqtxYXUCCpMxBA4Z0qEnemQXFxGkluvW2fn/WBMUkouRDrAKR/nHNarkR3uER3uIfwQr7VBfWUdz9NYkxHtXsXtfQUpwFmQyQA2xtU2rsDnxoZN3NlHCDvXmCUUx5Dp/L2RAqQweHVJuvUw3mYb4wTWSWxtBbQPvHbE4o2C42fhu77re0ZdXoUQo3+v1Wr8+I//b3fyEm+u3v/1xRHwpYsXLx6vfj4BfIASYnHXx19uJwaDhE6nnFTAzXs6TGPJAwiB96avAwfJYRdbNJHEA9xaRYVFvaREau8yLmyNt4vyNuSyf5hP9BPRjhshU9lE9MTW1yq2HB57Qnxo/ToDPe2DYItCgFmCnLieQA4HayE4zDxS4c/9SIldzPiPCIcmSkt6MYhq8qEq3h5PVLO1IsKypzawrXEvi7RCkDoJKz1Asps2lwqppiLEOEkqqu+DdQ6kNy67RZGJGrH1SIfpEi3F6KdIMks/NgySBGdi6skB8ZBU4NycqdUxFlqa+/XqbYaRC4A0aJU+y8IkOOUP79fMIZSH1QFOCNzwvrskItl9lcPnPs/OxU+zf/HT2Je/MDq+diDPPDT1KMqZSq6svYU9+3CltbxVHqqgimTq2oe/ghIOTxrE5qnXVP9wa/qKu3OSPC4tlXLeE+eOQ+k7+7cYfwpsDLUWkEcwninb+J4iFsvg9kQslt9ev/dbkIFPctiFay8XVlOI2RDw5GeH13D+fAhPAK4+3TbbDfLVjep1kLtVvhbFMGmMmwjzxlmGWyDey9up59cRrZyZIwTWZFBQ+TAZWndZPFVNEer5AS81IBYQAYQkDVZJ5HJKeuuqX4/i4szhZwuIRVk047JZxTY2Qeli0lWAxB0TUkmfxbX4HZt//8gorKiuOrHWgfAxIiB2PtnEZTsgs7maR0qBFA5fOnwJDdsn9lc5jnf4LiskB8455IJqELvIJh7AZgxWHsjDCBUQNsMJsEOHUqcDMr8JNkPYFJlFCJeC8vIohvJBe6A8pDV53T/HbqQpbka/piYs7sWZC3DyJAiHisrLTO0SRHe2fNWunHxNiYWUd6dw8w2Lu7zc9OLFi3vAjwA/vb29/T8DW8BPlW1/T6VClkFecnfzfOtGiYk6cQ7v3EPEX34GE0XIrTNz5Y3yaAfTXJuuYR9CmAw2zsDl5+cPfnAt9wk4Hmx3L2HOPIjcv4yo12H1DATNpb+zjWZ6lDiHa59AHBQ37hrt11hHJn16frHi2upgvllTGsGExqCuDb0sf1ytOTZtmgl3ewEuqRYwHlFjWT6dLSAWVbo2VzHBSSnKjBkBuGzXWK/p6hNMoG/Gka6DrE5d90qdQp30MWY8kPRNQEOkpWTYOciER2oFnnRk1hakRlxe8yIt1jo0GZn0mEyieGXiWuVV+oA4hrqO0i3GSFQAKiSMqtvKC+dwLsW1NjHxYI64C4Bh1ZNzeapGpj0kY18SZx1SSyZLgowR6GG/G3P2Uajn9t3CC5BmQcVHBYxfR01Y1zupcK3N1zxi8UYQbn7V4G6LoBTg4sWLvwb82jLb3o9YzOBmPB3m919uWykFjUaNxhPvRkhJctDB7lwuHjBqrfl/Oz7ObGXFECLuTztxAhaNcBaZGeTO80sNTp6nCH1BGs2fJ14UJQCcTUhWzpbWapssK3CXdPgTNrfCJhzrVqxz1ApO24ssi8KwQvkMlljV45hanc9CSTAlt04It4ATLHjthGDXrsESqRAhFYmdXNFLuq78Wem76WiNdaIyJeJUQGLzNXr+vwopJUpKpJRIqWiEGjCjiUhJQTr5HSuiEosGIBE2F7qTQl4JkjlBhiAOF6forNcgjSMsEuPVp9IjFrBCYYVGOYNKe1hVQ0djwm9qKygx46mS5AQpWzuNq41JsVnQNn6SNBReqz/9m2WNDYTSd3Eq5KsDzjmefvoLdLtL6JJe62tR6o7+3W7cU8RimffkRlMZxfsvmNwE1GoBrVY9byH9xAfQW5vEB11clmLc/A8tD6+Vdg4VvUPcxqn5a1nZQpw+h3vrk7g3vxN7/vFcxIlAHlxD9Pawvb3Sa5ZS0mzWqNUCDq8XRyWyNCULyicyAKzhqHWmYgOXizhnkUYjDayzhnDitsiC5hwOYIGbZWx9dvo1ZIF99dSxpKaKpIRe+avjyeoHbZmF4CDz2U1XF27nCnQ5R6ZeeB+EkPTt/L9HRpFRYJkuNImZvgcOSK0gsYLUCpQwox4LeSmwxsw4lfpkhT1KHAKsLbUsz3derjLG6HDE6FMkcVh+74yu4UZkxYFJceQup0b6OOkhpEanPYTNSP0mwmXj3jHSwxYMnbJ/hKmvwPrmjCFXuV+J88LcibYCszbfWWtrOPFX7nZLeKNUhFSh2+3yIz/y3/MTP/G/sL9fHeV6zSHknf27zbiniMUyuH1VIcUIAo92u4EQcHTUJ45ThBfgbX8tNkkxgxjXPcRl0yF9YVLc+jx5GH0+MQA7wD3ytcjz51EuBr+G1AK12oKH34StryKjLqCQnWukcTRHpnLiUyNNM/av72CS8jx4GlSbyli/RV9WRwmMc/NTj7P4aiKcLsYh88xYggJuEBtZOeAeRPl92o2q/RfcIn1FBXlQCyqCyiIdxxBAZCRdUyMW1dc5yIoJ0pFbmf9HL6Tsle8bDzNRguscpK6afAXSjLrOOgcJdVSBZ46eSHU4chLQCzbZq51jp3aGa82Hudp8mJ3mgwxqmyPxJDBnH14EB6QzkbMUVUgurJDl3iDOclx6reIjBJDpGokM8CfSk/3mSbx4Oi3oHIioiz19fmqcdo5KfUVWZdk+hJ6JSGatE8OS9vsRixtBNjOmtlot/u2//U1+4Ad+kD/8w4/foavK4aS6o3+3G/eJxQxulVhAcSpEa0W7Xcfz9LAPSTz14ur3fQd6dYX4oIsATD/CzYRQj9syF57z8BoiHE5Cj74N3fBHDfPExIMjfYnbPImTGtXvoPv7DPavDh0Vc5+PlZUx8en3I6IFXf8yZ+d6UEyi76+RGrAlTb8gj0jgF4TkJ6IWNksI9PjmajE/6RgLQhdHLaTUxMPqkUGmsaL8ehbpK0wFO1ikr1iE/PnLz38lWsFV3VtT/F27qYeR098vKYhKTKKXTZAL5VdGVoRw4IYDtZBENHIBrZvRyjiHyvLn1ug6u8EDXNen6YgWYvJeCIkRmiO9wvXGeQa1DYwOMRWr/dEpVMC88iMnF4PaxlSBp/UaCwWeOslNvIzyib0GvolH7ekzv0Uq/bnuqdYKsjOPzGX7nNSVFSFiweSdhc3cDG90cT4bDz9Co1HD9z1qtRCtX4OJ4Q0m3rx+/Rr//t//+tS/7exc59d//V/z2GPbfOhDf+UOXdkQ9yMWb2zcarlp/jJOhEGHOop6PWQwSEo9NMTKOuGbvpbkqDs8hsP0+7iJFZvs7WNXtub2BRDWIE+cwZ3fRtenUyaifzDV0EsmPZIHHkceXAVr8bMBh1deohYogsAfER9jMrqdfZLMVDtAOkfaKG4C5oTkQOapkkXljcYVuH84iz9R11lT44kry0xh9UViVGHUInbTk/DVXq1UtDppjDULISxxWrySlreqr4CZVJjkelqiGRCyMqqwl01GkgSH8SI9jKCX+RgREpvq6wzkcRtzTeSapEbS8OZFmBoLzjII1rmuTpBNVKEUpUcgf2aO9Cp7tbPIJdq0ZxXpL+Mgqm3lmgmp5022ZqDcsPOpComCFcARDKMTDkG3vkWQzaeBUTygAAAgAElEQVQuTHN1ZOk9/WXKz+WcQ84Kome3mTFJSxobXLu2RxynGGPwPM3KSouTJzfY2Fih3W5QqwW3TDZuTbx596RCjslRTiJ+jeee+zJZlvHqq6/wcz/3s3zsYx8BGDU1u2NQ6s7+3Wbcc1Uhi4jD7UqFCAFhGOD7eR+SXm9xu2n53g+hv/gZ0u4Av5UPqKY/QNVro9a2Re3DR/A8ZGNeqyCcxXp1xET4Vngas3EWmWX4SZdIaHZffQ6vvpbX+ts8d26P87u6DiU+BACp9AudOLNwFTs0u4oM+EKVivFGUYuZnHPu1uiBgDQeoGVzNPGH2tFPp3+vzEKgfZydnugOBtNX6JAcJQ2aejZUXf1aeJLSqg5PuMpUzKI0CEBsps8/MAGxbhIwLTKzLGhQ5jSpbODZHtILcMlyz3UqGhgh8WWMKajYUMJiLcSuQWIkx7Onx3x0QWI5CM8Qzz0dbvxslcAIn8t2kw29gy6YzBmeOXWyci6zzjII1/CcQWYVUT8kIusS1TZyBY+zCGtQw/cmbmxhlMaf6QWS+eVpPpmUn88ETXS/osEd5FVfk+dq5z4nzjmSJKPfH0dOPE/jeRrf96jXayilcg1XNnYPzRYISUfnfYOkQo7H8rNnH+Cv//Xv4Q/+4Pe5fv1fcfnyJfr9Lh/4wAentrtTeC3SEXcS9xyxWITbYemtlKTdbpCmGUdH/aVfUHHiARpveSv9L35uRCxwLicXzUZOWA6u5oKvGQtkFzZgbT0XQfbmhUhicIRN4nw/YxBxTLJ5nvruK6R9gVdbJbWOtLdPompzC60MUTmNOZuRBS10PD1Jd/R0njvTTbx02rp6EsYxZ/NtTYbnB6TDiSiUKd2hCNGVlJ4mTk1dr9I+sZ1/3I8SHy3rhHI8cRmqX3KJK5CODj8TtrxahMXEQgpBP5s//9W4zfmwPxXGT1jszLmbNjmlByRLWpg75+hGueYFfEJPU9NmSJYl1jkkhs4MhwhUOp9iEIojGoURHL3A58M5yFweJdgRm6x5hwQFz41TwVIhRgv0RA3p1/Bdgk6782WzyiPRG1PfI8iivJpK+fSCNjiHnogyOASd1mnahwW+MEKgKiISZWLs0edCzu2ftU8ODz0/8R+Th4nTo/WYbDQaNaRUM0SjmGzcLLG4VfH77cbxeN7pdOj1uuzs7PCJT/w+3/qt3873f/8PjBYBt2IxcFuu8+7vFXJDuE8sbiO0VtRqAUJQaRtehdoHvp3+01/AWTvuburcKNQirMFunEJce2m0j0PgHno8Dy0P93FZBoMe9Lt5U6Oh6nlyqPDkZ0jqTcTGCWqtTVLdIC/zhHjm0q21OBWUtgiHXMQ5SSyc8ugwLT6MjKKq3sJZgwob2JnSVmESnFMIKXBZjBYemRNY56h781GL1ICv834XAAdxeUh9L6qxEVoCmZO1tCINAtXkwFYMxmK2p0gBPE9DND/IOCQd26YlJkSEZrFxlEXRp0WcLGEyBSgpiSYqQaJUEqXj6/GULaRdTd8wJa8QmmvxCk2vWJ+jZN7srAxCyvH8LgT7rNL2FfVkmjQvais/gvTB5hU5ET7CW8f3NGlmcDgUDm36c+TIG3Zc7TVPgZB4WYyc0ExErdOovL5l/juooFJDIRf0RzG19lREwwQNbJBHR5aZ+J0rIhsCrRWe5xEEHs1mHSnlFNlI02yYCrnx8Wt4lpvc7/bDGIPWmj/+40/wT/7JT/NDP/Tf8Su/8m94+ukv8MM//EN88IP/MX/tr/0XWGvvKLm4H7G4jzlIKajVQpSSxHGC73s3RSoA9INvov74m0hefp5gdVzGadMUNWySI/ev4oQYDVruzIW8x0jUR0QD7KA/LfQse2GsQXQP82P9yW+iH38X2eYDuWGRmF8NW+WjKohFZi1WqFGnyjhYm1tNWgdWN1FZee145o5jEIK+t8FRFuCcJNSClhdh4y6hSulmi6IWGo8UpT0O+9UT0G7UYDMEXybYqv4gwpZqKPSCNEjx9DON4mk7x17SpBn2coGkEDP+FeXomDqBR7UxxxDGqnzGf+pP4NkvQDSAuA+DAWZlC+/UFubRx5EXHkF442dEmHhEWrUX8lJ3hdUwKydSCwSUFNyHI1oI31FLxkZx2YLoEgwrUdx0/x4HxBMTrhLzAkvhLCrpEtc3SIZaBz+diGx5dbq1NRpxcTpDFDQjO4aV3lxfoLnrnvExydrjqrCbLTd1zhWSDc/TaK0JAp9ms45SEmMMSqnh9ulNj2l3Esc23idOnOLHfuwf8L73fQBjDG9/+xN853f+53S71b/B64a7KcxzG3DPEYtlxJnLtj4v0lEoJQmCJVdRJedWT7yX9Mql6X+PE5zv5yFpm42jGYC89mLedGx4vbNfT1iLq9VhUFIv3+uAVjQ++3HSjTMMtp9Et06QzcygmTHISSfP+asnbWwQdPP25B1VUPIIxPhUSfJMlqH9Bge2xcB4oy8UZ47INMGFbNoDlHDDpkyOunb0s/mohac9DpPleoPsRA3Wg7zdfBkJ0LJ8ftbSjlbhx+m042fIUb1CP0Y/qZ4od9NVNvX1hVbck3BOcOWoxmajWz0Z9btEv/3b8Ju/Cldfnf/80bfR/7Vfyv+/1sgLj6Gf+Hpq7/x6zONnEJ6HEx4vdto4BFpmhfdK4CojOwBlXpuHtBGeI0wPcNIrrAaZO59cYCblXKFtvp/FOB3QnTDcOo5gOOBo5SwIMfq3ufP2y9Mg1q+jF/hXzBpnpe0Js7vbWG6a6zVSkokGaqurrRH5CEN/GNkQo/TJMTmZJRv5c393TJK9Xpe9vT3OnTvP+973AdI0/35qqFd73/u+eRSluK+xuL2454jFMliGWASBRxj6czqK2aqQmzr/hXfgnf44Zu86alLdbW2hglc4lxOHfrm4UuiyxtZ5RQnNdejs4+1eQv3Fb9F714eKja+8OpQMpACp9AjIW373RXFPjtRQ2NV0EvtuNa9MmLiVDgg9y+FAc8lssB5Goy6uueHR/KCWOp/9gb/0gmB30CA1ghPNPrld8+yO03dRkA9KidEcZAGDVJFNVGoILHUvJVSGQCeVE7sAOnH1hfZMwKoXFpqolaGfevQSxWrNQ4mCVbRz8AcfYfCz/zSPUJRAxb1xACLLsM88TfLM0yS//Isc1ULq738f/WAdTp9DnH6A5MI6cvPE3HECX2HS8hJM56rTTQdihXXPIhfllYawQlN1431ZfEIv7dFtnh6X4zk7SvVFrdNkKkBYW9iZFOkhKoSbBa4tUzBeHTURHXFCkrXGFWGvtbhSiJxETJKN48iG52nCMKDVaoy2u359h09+8pNcuPAIp06de82uCyCOI37wB/8rnnzyG/jbf/uHS7drNJp89KO/we///u/wvvd9M6dPj036rLVYa7l+/Rpf/vKzXLjwCOfOnX9Nr7sS9zUWb3xURTW0VtTrAda6Qh3FrVuCO4SSqEffivn8J2FicDJJiq6VTSgLzpklx8ucwo+tHQfhZdSj/qmPEL/zQ9iZcr/MsUDEaciCFomuNsRKZQOP4oHXqAadxKfuObKZMrAoMTR96CaS3ahG07do18fa3OZ7MDFfKSl4ab/FasMySBcPwlJYOmnejv3VoxahzlivRUhhkcM0R54mkaBCDnqObpp3FtXSoMQ8qXRIemmAcYar/TonG318mRROK0LIuf2LcC1eJVTl/TWm4TiM8l/s1cM6D68dTs+hxqD/9T9D/snHGCzIMbtLL4AfQDKfDnODiN6ffBIO9odnhb1ajY1f+VcIPT3MOFPdz0V7PumCIqo9sUZDDJCu+j44BGZB2WThMZwj0yHpRCmrlyV5hZUO6NbyKIY/7CkyCzExURi/jqm1c4He0KBLGEOKQEWdUf+RqdP7NZggFllra6pZ1OtBLGaPXxTZkFKgtabTOeIjH/kNnn76aaIoZnv7cR5//M08+eS7ecc73nlbr+1nfuaf8thj20tt+973vp+Pfewj/OIv/jxBENJoNGg0GgRBQKfT4bOf/Qzf+73fd2dJBbmF/BsJ94lFAYoqQ6SU1OsBUkoGg4i0xMfgdlmCp1/zHryXnsbuRmMykKa4MCgmLtEgH3hs8XUtimqIo/081TIc9FX/iLW/+Ah7X/9tuIkSV2stToeIio6UadDmsKJfBUA/sbSLxKBScT3N9+2ngpqenxiMNSghME4QG0kna7Me9hEug6E0VEnBpaMWmZMc9AX1IKts/AXHWf0J4WKmudQZE6S6lxGZ4gGg7hnigmoOyH/T/DPJ1V4TT2acanbnjLSyJaMQBkU/C9Bq8Ypdi+kurZc7DU42u3mqJx7g/YufQj39FwCI8w/jvvT50mMJY5APPoJ9tqRb8sE+nDgN13L7dzcYkD37DN6b3jy93aI26UzrIQqvBbiSrHLKP0S6ChMt6VUeSgk3inpN7SYE/Zmmef6w5LXXOjtaYXol5asijTHtLZKgOdeLwUkflfYw/iqmtZq/89Yh4wG6f5BHQGZKsifTIHBniEURrM3JxtraJj/2Yz8JwN7eEc888yUuXnyaT37yT28rsfjoR3+Dt73t7Xz5y88yGJRHhI5x5coV3vWu93DhwqN86lN/xjPPfIkkSajXG7z97V/H3//7/zv1erW77euB+6mQewCTxGJWRxHHi/0obu3cw2hJUIeNM0ipsNeujD/3a3OlpsfX6YIa9MvTFEKVm00La7H1NqozVt2r7j6rf/ERDt7xl6fJhfRQVBALoYnxF669U9XEnyEWfdpTE6FF4Vw2Rdasg7pv6MR6WP0BL3VWCXVG0zccDjw6ST6RQ252pYTClBaJ5jALyje1dJQdouq7BtrRT8cDR2o1Lx+1eaB1xKS6sZ8u9zoqHC/sNXj0xFGl0BTAzDiIRplmkPmE/av4P/cPkK88N/rMawQsioPIWr06AbF5YkQsAJKnnpoiFsvoK9Js8YTm+x6kiivJGqeDfYQtJhdOyMo0iC76QYUkFQFiJpLhx13ScIVowiFWF6QF06CVl5KWEaiZn0wIAUpg6w2SegPn8oiGCVuILEGmMVnr9SUWt+K8ubW1xdbWFt/4jd90W6/p+eef48UXX+Bv/s3/li9/+dml9vn4x3+H7/3e72d9fb3weu4Wr443WrnpG+vbLIHlGpHlE3VRX49lz3HzUYtxOD19/C8hggDCsVbBVugoFn65NC6vEAHI5r+f19ml+fynp46dGVP5InRsG1dhl32MQeqmmmgJqTlIp/eLM/D1/LmSzNEM8kkhsxZfWaJMcxD5DLIxqTjGfl/iq4rSP2HpVFb/OaISN0otDVFWfj+K3EFB8kqnPQqZSwFJgc9GEVIjMU4SJYu37xWUmV7fV3j/z09OkQoAv79Ea+/OgmZNMzmM9DNPTf13wU85jQX6imMko2yK4Eq8hiqwg3ewMA0yb7ct2LcbiNmeJ86ikh6d5rgyQ1ozZ+0d1zeIahulpMI5t7DM1Pk10BIXBNhGi2TzLHamu/HrEbG429qmf/zjv4vv+/zCL/w8n/3sZ3j66S/wK7/yS5X7HBwccOXKZX7mZ/5vPvvZp9jb22Vn5zpxHPPhD/8yR0flnjqvJ95ovULuRywKcNx91BhLpzO4iXru5apKCvecJCWrp8ALUecewjz7dP5vgz6usYkoyHMTD0B7hQQBcrrianXolajYOwe4sIbIpldq3s4r1LZeYbA+FmU5r44oEnEKyfW4iVaSpp5vbjaLRDYIhg6ZecOt+R0GmcSX82WeaWZp+IJeImkHCTv9kMwKVmqG3d78DNZPNFplheeYTYPMohVCLymeFZdLgxRB8spRmwfaRwsC/9M4ivLX9qX9Otsnj4allPMQuNG2kzjx0X+MuvzC3L97gwPYOgXXr8x9NsKVVxDtNu6opOLh1ZemtDzpF7+Ii+OcILOE5blUC70+AAYT3hoOwcu9FqdDizATTpR+jSwtP5hWYqgkHuOQ9bzSZIYY+CYmap6Y8s3wJ9IgDkHUOkXk1Qkr3D3RASKpWBwMjzYJU9BMrUIudVtwNzpvfv/3/9ej/58kMYPBgO/6ru+p3OfNb34rH/nIb/DMM1/iYx/7CI1Gc9i1uclv/dZv8sEPfstrfdlLYZlS9K8m3HMRiyoctwnXWpGmhm73ZkjFrVWGzOo7soeeQAiQW+NQaFHLZhiGVIPqSEGVsDTXYcznG3X/kMali6h4PCAW9vUAUtnEokiMQHuL3R4jI/LSSSHYS4urSKwjb8RVcMLMGBq+Jc5gJcwJVS8Ro2jGJOJMUvPnV/DOudIuoccQrlxwqCu89gPtSG35a+aG5CLKlisflcJxMNCjfY+i8vSNkvk2k2g/9RFWPvub5cc/VdXefvj8nKkQuvW7qAcmqgLSlPSLXxj/9yL/iiVCwlJAamfvueRytEYy0Q02XRD6CGYO0WGNvgmpq3nSrkw6Emwewx9a3Dsh6a08QOTVwbniKpFjLJirHXIu1Wlr5S3g7z689hPk7/3eb/OZz3yaL3zhc/yH//DRym2/7dv+U77pm97Po49+DY8++hhbW1vU63XSNEVrjzBcHFl9PXA/YvEGxKyOIk3FUl0oy3ArqRDnpjtg2gcex734FPL0WezRIcQR7ugQwpIJZYHinjTOS1ZLmu64Ejm+MZbVl55i99H3gJA54dIhzISCd7Oxd0Uv0YRycXfKVDfRLsVWpBPiDAKtR226J5EZQ6ghNgwjGBolLbkjxfQxdzqCtTokE18/0IL9ftXLVZ4GqemMXkWJ6LLdTF/er7PZShf6MuSVJ+NruXRY5/GTB4VRi2xm8g2ufJkTH/3Hlcf3PFvQ8WPmuNKrtKWSqyuYl8f/nXzmKfwn3gHL+FcscD0FKsnHTtKm7WkaHC2RBsmfdakUPbFGN86JsC+SOQKQ+M3p8zqHjrs4oN8+M6oe0djy5mqOyl4lANYLp8pMrQ5xepqg3y3CzTuFD3zgg6MeH4sQhiHvetc38OY3v5Vmc7pS7b3vff/dQyzeYGv8e45YzL4vRX4Uvu/dlkZkN7k3U6xfCMzZN6H3XshTIl95BpIYt9JGFLUzT2LwfEiLZXhCCFxYz02xij7vHOBq9bl0iOzs47uY5rWv0D35GDAv4pRejU5vPAj2EkkYShbFtqNMkLrFyuw4g0bgkSRpHsURgsz5JGYo6PQc1mU4LxdCrjUMewUpkf2+x3o9JTE2d9I0ebRDC5cTEpELPlOjiDKFp2BQElHItR3F06yvHb148YDhS8u1JKSdGbReJGycP95uL2S1Pk8HehPdTOWgw+kP/6/ICjdIgPDwMnEF8QTQe5cqF962P2Ps9FSus/DG/cqKUa6NnUJWEQECOErrpErT0FFppEkAWZKQyjp7aRs7qshxSJdNX6bwMEzfN88kCGeImidI1PiZ1xXOtE4HxenDyVPNDFCmIFrxWrc0l/Lu01fcKmZJBcCjjz52B66kGPYNVhXyxqJJNwCtFe12Hc/TdDp5m/BJk6s7RSxm9xUCvDe9CwDZbCEffgwQpS6OQojca6ACVZcmAFuQDlGDDpkKaF15Bm/YvyAzZqq2fjebbe8tSN3iFYGSik5FL49J9GKH52mkkPQznygTw8oIQT+VxJmk7htCbRikgmY4eaMcShpqOsWYjLYf0fQTmkFC008JvQxP5cZLWkBNG9ZrCQ0voaFjZglSoBaINiscPCeRDEtYLx3WqPnVr2Qnmh+ArnfDuQiCwNGZIBYnfu+f4R9UaCeOr9nE2DMPV26jj3awGydLPzcvvQQT3hXZs89iewOO0hq9rE5sQzIXMLeuWXJwXZS2Asicx6u9da5Fa2RTnVUFCImQmkNxgp10bYJUQF3Fc2XAqZ4vnQ7MgDRcZeBNTljlaRDnHLKgU+zUNkIiZiIatlBfcfdGLO60g+VXK6xQd/TvduOei1gIIWg2wwV+FLfe4fRWUiHH+x5HU5IkIzn5KN7Oc6h2G/fwY7iXn8fVa8Vh10XuQmmM8wJEWrK6yopXeZnJ24KvvPI5dh57LwiBCpuY/iFOhewM5slBN1Gs5Z5TpRhkPr1EEXpq6KBZjTgTpCZASzeV0oBcBNVPBFJYApV/uBYCwqGOe3mIXKuQGD2KDwnhhk6OeUuqyQyGFNDwMwJtOIr9kbNmzTP0E4mSxwZagswKhBAoYektsOfOj+3Y6Yxfwxd3fc6sRKVW2AeD4sjJK4d1Tq/0OL7Rk/qK9StP0c52Fl7LMczKOvLl6m3kydOwe7X4wzRFXbiAeW5YdWItL/3x8zS/8dScD0jLi9kMO4BZWl9h3eLtjqMaifW40p+3ll+rJROVJWPU5EQaxFq8QZeVwVcQLstdNp3JUxpKEwVNdNIn8+sgBL4rMyIHdIBcINq0uoZKx9tYr47T8ynPu5lY3MfNwb3BCNk9Ryxy97hpq9r5bW79HLcSsZBS0GrVcc6Nq1LOvgWuPQcK9MoKmT2P63emm40NIUyKC0IoSpUwLCVrraL2iicGcbSPqzfmiIfs7OJaTfzBIfW9l+hvPEiUGjRwPdsoPJZ1AitCZInvhQB2humTg4HPajhYWCFhnMdg2Bek7lmksKRm+n7XPUucOowDKyTWKYzLLbZ9aQGBEJN8R2BRudDSgS/NXGWulo61MKabZPh+yNHAIzHTNuJSOEJtkNJV9hw5Rl7tMj5RlEgGqcZT87Oep8pzsd3YAydhWNpqhhOrzCIe+fy/BBmxbGFdSH9hSkKJrHIbUZ9e5Xtf/DPib/jGue06aUAnDWj7A1aC6jLMHEsEWZ0jLjEyy2Ep6BQOgCZBZgmN7hWC6AjhbE72nZ3ukWMS6kmfeuda7u7pBTgvINNhXpk1A1FiXDe6ZECa6e+fNbcKt73ZBmTL4j6xeP3x1eC8ub29XQP+FPjYxYsX/4eqbe/JVMgiP4pbTYXkuPH9hRCEoY9SiihKpqtShCA9+djohddr67iVtXKmWzC4TULOiCDd1BQLpj6/ylNRj3SYT25d/hIiS3InznCdw5KKDoBe6pUOhELqkYmTsYLMVptUBZ6ml4yvtZ9KuonGOIWUCiUldS+vxMhQGHSutBf5t9SyXO+RZBIpcuFubDVJgWBTCGj4hiRNhlGF6ftvncjJUj9kkCl8ZSoH6Sid//0uH/h4Yv46jav+TV/Ya4w8M/pDj4vzz/w7wmif0A1INx6o3P8Yze6rc1busxDXXqn8PDqcXp17T3+qkmR1k5Cv7K2zaEhKl4hWaFldvhfq+dLlZrLD9v4fsLrzJdqHL6HTCKc0Vns4pXBSYkveNYFDpRF60CHsXCPcv0RweBWvt4dKI6T2EbY6DWK9+hT5sCrABu3CbYXgNdVA3JqG44218n69kC9D7tzfkvhx4NPLbHjPRSyWwe3RWNzYPmHoEwTesGOgmGprfAx75nHYeY7jWK1strGrW4jrlxD716cfjxLxJoCtNXHNVez6SaSWCKWROncotInBJjEuM7iOnjMQyjKHL/Pyu/aVixydf4Ir8Xrld0uMAN+Hgp4MR/G0BuMw0mw2MmxBWaIAjgo0BpB3HM1sHlXIrCh0pAy1LSU4ZqbHi5IAkl4qqalsKnohBTS8FCXylfEgHRpyOUczyDgYloBmVrI/8Kl7GVqauSoNLS1XO8Vk4fJhyFY7nnrpd46qH6rUKBLjo2XCUexRP3qFB57/rfEGm6dgt5oQ5N/akZ29gP9chb13rwNnz+e+FQVQrz6P80NEkq/CxQvPwtEBtItLJz1p6TnNl/dWubB2hCxoYw65c+hiVN+nQNmpVNNq/CqnBs/hlEQdp+KGv7+zJk+LKQVKYRBYIRHOIbMEaQ322ORs9MzmaTGjfFQ6QKQDjA7IGmtIf5i+jHu57wzH0YrpxY5pbpXmU+9Fc6w3Ou72iMX29vZ/Cfwh8DaguhEU92jEYhFuSyOxJff3PE273UApSafTJ4qS8n2FIDs5VjJLAKVxZx/GPva12NUNXFjHKZ33/AhroDQ0WrjNU2QPPY59/AnkI4+jT55Crm+iwwDlqeFKXaJDD7/dxF9fwb75Cczm2alL0J3d0aBW332R67uSna5GF7pLjtFL/blJXUnJ/mB+oijzZlBKlbYsP0bNc4Wkou5X2/emRheaknoK0oIeHlJA009pBimbjYTVMMbBiFRMop/q3JxLTIfDhXOlqY1+qqemRyUcnXix18ULOyGh72EtPPq5fzEVvq/Xln+mVXNxlY5YKyeUwhrM2WkRqPzCn5duPyZQkuf2V4mz+fu4rL6iyjcEmNIlbSYvcTp6DincmFQMkRMIO7evcibX42hNFtQxQQ3j18j8EKs8Ur9O3NzCKQ+jAxygshj/8Cq2d0gaR6Qo0toKtrWJaJ9A+MHYT0D5iNZm+fWLxb1UbgX3UyGvP5yQd/SvCtvb228G3nTx4sVfXfb73I9YFODWG4ktFm+Om5oJ+v2IbJj0FUJU7mtOPoa+9hXEcBCUWYxVdQhquAceGQ831kCaIpUEkYfnZ3/ssnr7/DNwXoB35gzp2hbmlRcJBvvIuE+iTxCYCAGcv/rH7J7+K7lfQ0UaOc4kDe3DZDcK6VPEbRMjidKQ0BvnnJ1jqt9GERq+ZVCQWgAItC3TpGLcsA9ICYQQaMmI1Agc2vPpxbmg1VeWQFvaYUqcKvoFq+rUSvqZpqYNxkmUsFztVKd9XtmrcW5jgHGi8reahENyaU9y8uU/ZGX/K1Ofrdg9rnkBsky0O4F6ujflZ2FOniN85GG0Jwg8i5Bg/TrxyRbJYZ/ey9dQ116ZLpcMptNj8gufwr6n2H8gnqmuefmozbnVHoGc1BAtIe7EMSjxHIFcSZNawFrOmBdoR5dL762wi1xFwEmJmog2GC8gra3mzpjk4mCjg/y+OIvMIqyUIDVYQ5YJnHUIJHgNkIraxmkaq+2cSGcZaTr+M8a85hGFm3cNvh0p5HsTdsHkfofxnwHR9vb2/wi8F/C3t7d/+OLFiz9dtsN9YvEaoNlJIOcAACAASURBVOoFW9zUbMHLKQTJg+/Af+GTeTWDyYqZjFTgCVyFUl1iMTpAFbRtBlBpBFLg1Tz0I4/Qf+ky9aNX6ceKYPjkrMaXOdF9ll31GIHKKvN1vcynqcfEYrdfXhbbTyVCBAQqBpH3C+lH1YNWmeOplpZ+XB7qyE21Kg9NP9PUdYZ1jm7iM5iqzsg4jDy2GjFRplivJewP9Fw0IjUSiSPQFiXcwtV35iRxKtHaMViiwuQY+9cjnnh6fnGhhCU7dQH/5acXHqPWv0Z/dQt56ixr51psyl2EmO4lYswhtmmRtRROtUjd29jLVujspaQvvog4nO4rIj7/qcJzSSy9AjL28kGDh9ZBk5OLZfQVasEmdc8greEB8xWCtIMsqUKyQqIqPCkAjNBTKQwHRKfeArU2K3Wfg6uvItNB3sF3IqUorcEhsNLLG45NlDE7v0nPaHq7Bzmh1QrP8wgCn2azPvKYsNYSBD5ZlmEWte29QdyPWLz+sEt2Nr4TuHjx4k8c///t7e0QaFaRCrhHicUyEYVjcnA7mbvve9Rq02ZcRde28PgrJ7HNTVR3Z0QuXJFYU8r8u1Yo0q3yyomFScm8JsokCCkIz5+m/6Il7F7FrTRG3/Fc53PsNB/BDwRxhfFnnEkano9wCUrKQk+GSfQShQgCfBmTLhAu1jw7rNCYR91zRCV6Xefy8tVlMMgUxoo5s6xBpmn6GVe6NdZqMd1Ys1bL2BtoZlfZsVFo6dgfLDeQXDoMeGSrz5VeuTh2EgLH2S9/FC8tLm3UK21YUEoKYLbOsfUNj7Fx+AywR2F/FWc4aJ1n9SAvK/VEyklvh5MngZOrdF2DQ/MoNoqIj2I4OEQc7uBWpsP8niy3wH9hr8GDKxmeSpfSVyzq9hoy4LR5DuFMTpxLYJyodBd1ANpHTGih0tZJbNhGSYmuN3DNrXEQz2aI/gEi7aOyAcJmCERexSOGMRO/iZswxHLOjSIVxxBC0G43kFJSqwV4XhMhmIhqpKRpdksRDSkF2aKcYynuRyxuBl8NvUK2t7e/E3gfecTiuy9evPgvy7a9J4nFMjgmH7eDuCulqNcDnHN0u4PbssJIHnwn4Rc/lpfBJTFO6UK2ZKSHrCAWyuZRhlIb4sltpSA8f5b4xZfoihYtchfBdnyVU+nz7KUXEAXVDJPopz4NnZC66jTAMbqxYr1ZYxAbqgYtLd1cySkMQ9/ZsfHZ/C0KPUG/JH0yD8FBFFDzsjkhpnECTxr2BwHtICExkvUCcqGE5aArK1Mv05Dsdb2RidYirCVXeNPO75Z+3vIGLGqBFZ19nIceqdHxPRbVqDpV/js2RQ9On6G1exnawAMeL+1cZH+GWCy6Ey8ernB+5WgpfUVRJc8xhDOcSp/LXVuTZOhbMo9M6KkGY0WwfhM14aLphCJZP9aUFCxIpMY1N3EMbdacAxMj0hgnNXjhUgZhzjmsdaRpSr+fX6OUEs/TeJ6mXq/heXqKlBz/LbtIutlUS57GvfsnyLsRZf2f7iZcvHjxw8CHl9n2PrEowTjqcPMRCyHEcFWh6PfjwkqP4v0XkxqhNckDb8N/+SkkNu/BUPBSK5thhSoN+QoBxgvRJY6BKu7jtDciHkoJ/PPnGRxEkI0H1o3ei1z3zlGryakJXpMQiJiAGE+kpMZHKs31/nLEAqA7gMOBz3ojwx2bXE3AV5bBTERCChAIpFD0M4/UKuIsXxlr6ah5Fk9ZzAJ/gWN40nK5E5JPGmKOpBgnaQWGvYHiKPbwhEFLhuQi/64Ch0kdh8M0yol2Si9dLMjsR3kVyjLbXrj44TkR4iQa5ojD9ib6qNgwK3r067lwOkMJQyvbJal4dgDq8SLjrekfq3Xpc+w/Mu1nUd79dYydfo1WkFYuiKVwxBXCzcf4ElKAsxZtyonDIjHbcKup/0pbJ0cka6kFiRCgQ5y+8V4V+fHHJ7DWEscJcTzO5yl1TDY8ms06WmustaOIxmwkZPr491Mhrze+GiIWN4L7xKIEt8Pkqt2uE8cph4fLGP9MHYGhfLJ6q/UHyA4u4XWuIbIE5xcMUkJglFfdcbFipSSdJdbh1ApOa0Gw3iTZ6eLb/LuF/R3Ot7/CgXuQFd0hEBE1F6GKFJ0GVvyrpL6Xl1kJybVolf2sqBTRcRQpjBNc73p4yrHeMMMumbkBla8cqZFYBJmRDIbW3gCrtYz+qMV2/ntmVtCJFb4S9BOPtZpBibQiP+Y4ij2OIw/9VLPZtHRmftZBplgNYw6iACEllw80nrKs1hL6iWS/p0nNmBzs9xT1wJItWIlf3ssnzbXVasOttYNn2bpaXWYuhMCeOAcFxCL92r/Eo2ud0XPvuZTD1XM09l8oPV49OeCofoJG/1rh5+HR5an/bl3+PFjLcQmOFMX6ilkkqeSZwxaPn+yUdp6p6vf2gHueQObsU1gzURo6DYvES/uFnx3D6BA14aLpgGRlXD11NzhjGmMxJiGKxmQj12vkkY1aLUBrTZaZqTRKlpn7xOIOYJlo3FcT7klisZSO4SZtuT1PUauFCCE4OurdVEjxRvQd2bmvQ138XWSWkAaN4tXlglbVyqZY5ZU2qJIFHVN9aeiefAj/8pcAaCa76Oxl6jKvydYuK50CU3TeA0VYnLNkTnE63KVl+rw0OMVk6iDUju5E99DUCK4eTTTXEg5Pe4VdMQNtK9McvoI+gv2BRgnFai0B7Byh9KRjJ5mOFuz2BE0/m0tRZFaipSExihPtlEsHAYNUUdcZqSkSc6ZUVTvUvIyjYefVs5spvYIyTACc5fFnfrn0OFPHbPpzdC/efhePrneZDQm4ehP2q49nGutQQix03CNaPTMiGDruUtt7gcHmBaBaXzFxFRwO9Thfutrg8ZO9QnLhSvQVa+46q3Kc0zlusGekJguaOCExQ4KLs0hrkFmMTvvogv4eTvtTXX1NfR3njTUwdwOxKEKWGbLMMBiMNVVa64k0SohSCnDU63nbg+NKlBu5tvu4cdyPWNwjuNGIhZRi+DLm5aPNZu2mBVQ3QmqE55M8/C785/6klEAoZ8mUXzhI5gcRGC8sJRY66ZGFzbn9PU8SrZ0m3B+uSqOIWn+XuL5e+ppEBHhyPFAJAR4Gi6SuIh5rvsL/z96bxNqWnud5z9+sdrenvf291bB4q8iiKNGkJKqxrAZy2kEsGUIAT2wgychWgChAAg8MBAEyiAfWIBl4EMDwJMkkSIAEsB1FoC2royRaJEXyklWs7ran3+3q/z+Dtfv2dLfqVt3zAgd1a++11r/W2qt5/+97v/d7HG/Ty0vnx9mX8SzqvqG7pGKi6hV0ksXfWWvpTzh4FlZw2Pdo+ilaTZ/HXjp/m1gryn2b+bEKK2n4OYd9RS9z2K6kHPRcCiRamrnOnMd9h916Si9bTBhMXsBARvj+U7i+Y0ZOpZO48eybNNvvLdzGLOqccDTh0RBfe53Xri2OqoV2nSIDvDWN1nO/BhORi/rj74yIRdDb4/OPvkE9fjogxbYsvywyEIpM+3y0/TN8T/8EuW4CkgfPKty/3p0Tai7SV7g25oZ8MroecyOQ2qMdbqIZk9/hmpZBq3vXJ3d9UiTGChyboaMTpClQyXSH0sloBXy6LLfzPCfPc6JouG3Y2mpSFMVUJUoZ2cgmyl4vtxLlZcdVxOKlwemJRRCsKh89x8hnTcNUNkhf+RrO+9+kCOoLoxZWaljRXVEVGUaqhUJPwWJxkZt2iTevk/dO0GmE6rVQYUCWxWROWJoJTaRzEly0XDz7kRicwTz0XvCUbhHyNNriOF7dqXUV0U9XVHtUXLvQxfMkdtkIEtRAXKml4SBZnAePc0XDz+bapvczReDkRJnGSomjDEmu2Kxm7LXnz+NRV1PxF6dEnhyNj6GXSByRUdjpcyJtzhvv/h9Lj3UWrk1Jtu/h779HHja5+fkNlFh8bYR5i2N/iyA+XPg9gN96SOpWcZa0BJfJNDmpPfo2+uYtbh/8GV7WHv2E1lowBjG0sbc5btrl9ce/x2v8Hrn0OPZu8kH1SzwwX+Jz1xLEIOKxWF9huas+RA0IVCocCsfFtzEOC5xtEegZci4xpS5DSNLKJlb5CFuUoukiQ1hDEUx39R3axz8vPM+IyNAcsNeLR+0EhBCjqIbve9RqZUXYkGQcHh7R6/XY3FzcL+gy8OjRQ/7pP/2fuX//Tfb29mg0Gvzdv/ufPbfxPm4UnwLx5llwRSyWYJknwiRct8xVriofPS/OHFGsbZPd/SnkwfuwgFioIqWQGmWWCbYg82q40cnC7924Q+EFU+sLLFhLfP1zVD78Lk7SJSkMXtIh9eoYBBmyrNm3Ai2ylWdUAA4ZmXWp6T6VasT7Yof9aL5vCYCjDN1k8Q1Z9QqSNdGOZTiOPDaDBCkt+ZptdBKNp4uZGYcYtG0vUyM7tTIl0oodtqoZh93ptEpuJI5MyYvpqEXo5Lzfnx7/x08k926YKXfJz/f/AuOGsLqQYQpicxd78AGVn3ibimwvX04I2v61lcRCYombt3D2Hiz83j95ROEGqIHOp3LwLjc++ldIPUPsjCn/Fu0H4JiE3eg9NpLHfOXg/0F8YLBC0a/dpL9xl47eopAOJ/VXQUi25CGBLfUSsQyJnSq17Gjh9k+Dki8UCFNOHqyU5JVF7eNfzFTIebdfNm7Mpho3Tlai/MEffIPf/d3fxfM87t//Am+9Vf69/faXCYLTlUmvQ7vd4td+7df5xV/8GwD8nb/zt/n613+BN99861K2/0ljWRrv04qXklhcVGOhlCQMy1nssvLRi/pgnKsevHEdx3XIHn1/XpwmBEa5qEW9ogeQRbq09FRgKaQ7R0xUFmOCGv3te1QO3ockQSuJl7RJ/AYKgwGMdCnwyK3FtfFSfl6Si5TUuGhpebWyh7GSw7g2t2zNN7TjxZewp+1SXwuJpR8brmcPuZm9h8xTgqJNKn1SEdBydvjAvkUzLEYVHctgrFjYvj3OFQ0vpZW49DJN1cvpJpo4V3i6mKuEOOg6bFVz4mJ8PEkyToMMkeYCTAaUUQu/6PJm9Kfs1beg9cHKfZ1E6OZkX/46u95yUjFExVlfzeTkywWPwlqixi0qB++MPss7XdyNMWHMcNDmFNE+18VJx6kXay0y7VFtfcj17h8DcFR/nffu/Tq78ikAPV0n1z6qKGnuIhjLyM12Gax0RqQCypiE8eavy+f/4r+cMvjl21+//5OVKL/6q3+TX/mVX+fJk8f88Ifv8P3vf49/9s/+F375l3+V3/iN37qUfXrrrS/OjX9ZpOVFwFUq5CVBWdkx/WNPlo9GUUK64iU9DCmej1icTzgK4O7eITaC7OB93LQ7RU9knqwsPVUY4mADaQoK5WCVUzoQ5ik6j1BpHyuniYeT9Yi9KmxskXf2Ub0WNgzw42NSt4qVikx4aDHywya1IcpkOCx+kQwjF70iwJFwt3qIsYLjZLr3zTL9hRRmSj8xCW0S3kr/HRvxR6PxW6JJxXSomA4A17IPeSX6Lh+mb9P13iRhNbnoJJqaNy/kLEmawSKpBQXdpIxONMKMvfZsGkaQTfwsnir44ePFx/fOY8n9uzlxrnm7/4c4NqNWXZMymkFRabDrdU617LY44MjfIlwRtQg7j4nCLbz+4mXUjGFX1u7iXr9WOskKF5FnYBSsEgq6HqSTeg6B3N6h5noYDN3w8yiT4lh46+D3sLu36HpbGO0gYFTBtAgpHuEahw8r9TSxcCulNfcMXoQX/8cNIQQ3b97mzp3X+NVf/fXnOtY3vvH7/PRPf5179155ruN8nLgSb74kmNU5eJ6D77ukaU6rtV7QdpF+I+cpdRVCEIYeSkn8zWscJAlxFhNEh7iD8jkhBLnycAcPeQsUyiN1KuTap3A87KiiY/zgygd/WIspcsL+Ac5AFS8AkSfg+iS796h89D2SwiAV+PExreDGXKtyJQxWKlIjcJnP7RcoIlElF5rUyvKhVe2QG0knK0WdoVsMuorOo+YZonz+pdzI93m794f4dnp2XbUtCtRUaaxrEz7X/XNudr/PD2o/y557b9XZJzdi9Ls50pBl0I0FWuQoV5YlqgMhZyt2aAY5JzMN2NqR5uamoRVJTJ5jl9j8Wivodgu21RGvxH9VHrMTs6/rhPn6CEQuHDZfv8bRQYNb8btrlxdCkDeuwQpiIYQgq+0sJRbe8WOEq7GDnjjZSRub56AdHBOXXXQdpyQPUpYvzjSFfPAid5wZUgGiuYFwS0IlKZvF1URcXpQ59Po1TOU6UHpXOAu66462taZyykJpzT0B4y1O0b2oVSGnwdAy/Dz4OCpC/uIv/oxvfevP+Af/4L967mN9nCiuUiEvB4ZRA60VYehjjKHT6Z/6prtYQ56zret5Lr7vDISjpZ1vUG3S7xzTrd0s6/ZNjjQ5mJzEq2OUQ6GcuXEEZTmoaxdEE4QA7dBp3MGN24T9faQ1OGmX1PEQQYWkvoNNEggDvKSN421i1PxsWogyR50YF2+CXGQ49EUNhEBShqgBCuFws97jw5Yiyj0CZz79MMRcl1JruZv8gNfjv1wYClfC0tKbNPP9ue9C+txLfkCFHu85by0NJUWZpuGnWCt4f98hHaQ6tDSkqWWzWhDUymiKsXJgHTKf8jrpCXyn4J2Hq0OjDw8lv179/dHaQgi6tduEx99buR7A/s5P8EaY065U4ZQWK1W5nkyr7mr9gvR9iu5gO9aSHbfQN24g44ltWwPFoPmXVuA6IAZEQyrIsrLBXqWKCKc7sG5yzL7YYceWv2N48phu4zaFG6LNcn1PbiX+mhNhtYecsL63QpURiwX4NBOLFzEaMsQf/uEf8Jd/+S1++7d/h8PDA54+fcLbb//EJ71bl4IrjcVnBKdJN2itUEpNdR+9zO2vWvc0KEmPhzF2RHrC0CubF7kBru6S5hlWKgqpKAZ5eWENcmVzMksuNNrOp3okpS1VFtRpeyGV9lOcPIKinH1mWzfxnr4HYYAAav1ntOp3Fp4MIQApiXKXQKYkxqEva8iJZdXgRczAyfR2vcOPjhRRtvjFq+V0GkRS8Eb8LW4nP1p5Ls0Kk7AwPeINcUxounzP++pSZ8YsF3x44EzZfedGslVLeXLi0IoMNzYyDvsevVSzU8vY70wLOfuJwCOjMKtvzTfEu2ylj6c+c2qVtZ4TJ+4ur94p/71bTzGHcqm19SQqpsuz2h3qnbLRSOw1Ka7dw/MlWV76ifjCcGy+gOx3sFEfv/sMPxqTDTPj9JgeneBu1FcPbAxoiSiKkoO5Dpmul8e6ABucYIVAWIvA0tj/IUc3v4xbLCcOGe7CyNnK3fJqS29wIZZqUF94vKjE4gc/+D7/6B/9t9y//xZ//+//F8RxzN/6W3/7M0MsrjQWLwF838XzXKy1tNvrZ2qLcVHnzhU9D0ZpD0UUxWQTyflJQuPVt6FzSJpNPzQtAiM0cgFxGAyAtSwVcipbUEgXpKbbuEml9QSd9il0A+G4JJUtdGFRSuDkEW5aVoksGQqhFN0iIJNB6SEw870tdwYhBErCqxtdPmovcuksBZ29tDx3ipwv8F20Wt8mvGo7GMTCiEZAzLG9zu38xwS2x7/zf55cTOsuBJYnR5qaV8w1GGvFDqFb0E8VH+5rrjViurlHlKs5b4vNsOA7P7LUavMCzyEUBX9D/9u5z3dqCSmriYK89xpalb974BgeOjfYzR4tPzETMJUmbalRm5vseC2U6A13aHwehE9Tt8veINe2MHmTvB+TdXvkrQ7CdbCD6oL8pIXJMqSzwqpcO+N0yABOtUJXNqjZ+bSPthmJ38CLS0Msv3+M2ztiUY++yXVWwSJGplpDGH8VISoLtJ8HXuxoyPObdb/55lv8q3/1b57b9j9pfNY0Fp8tmnRBuK6m0Sg7B3a7q2191+HclR2sjnb4vku9HlIUhna7N0UqBmuPxhVC4Ne3CavN6X0RArO07dhoEXKhS8vtRd8XKQaBEJJe/TpgMUPhXXOTfMIJM+wfrJzCSWHpmPrSSICWdurl68qchjtRW2ktjjQ4FPRjQRQLWh3L69n32OAYX2eYNb+FI3I6anPp98kggrBVPOOr0e+jZ/L1riw46SsOOqWN9ySMFTQq5dnOjSRKBCZJUMKwVR2Tu7qb8q0fZGSFoKKXC4N/Vn2Tpph/qfracBLeXrre4fYXubkxEzUIlx/zJHLp4l3fYet2jet+C7XkdDbtET1vvE2pFW69QuXmLvU3XyO8e4vg7k28G7s4Gw3yVfeZkGUkbBKVGsJxiEW4dDWVR1PXdu1keTvXzOq1Bl/SC6buFqtcWNHj49OcqpDyxYxYfNZRWPGJ/l02riIWLC4fLZuInX+bF0mFLIp2DLUeRbFa67FoXO2FVB2fqN8lT3oISmFpjoO2y3PPQpROkoVyy/SE0ijtIKWCPIEsxVgDEnr1m+h+G6lASEkR1iArqw60yXDyPplbXThOO6+gHUFUuFT14oe8r3OizMHVBiFgO+zRjTVxpmlFksIIql5BZhWSgp+rfIfrTikkdKTlWGyxZVc3zMqVy6LWJgDVoj2amTfMMV+J/jV/HvwShXBwleHdx+WtlBtBxck5malYOe5rGmFOq685iRzyJOPDPcuNTUPgRTw5gPe741/i0aFkq5nTz6Zv0R2xz8/IP196DFltG/ofzn0eqyq7d0JmjZuaNdZ2MI2dGubGK1x3++xlN/E776xcvmK6C9QjDFJ0GjxnnO8TYqEeyVJeR5PEIgsadG79BFKCYy1Ps01UnpDHKQ1OCPIOAtB5SurVcJPy+vOiY7JsF+vMa31yq1hbTzNDip36Ftr3ltpdP8+qkI+j4uQiLdevcD6YBS0JPs14qYlFWT7q4jiaKEqnDGAuJr68aBMzmIw6LEt7LBt3URpFSkmlWseEVfq9NkUaIYQlx0HaAoXBAhaJUA5SO2g3QLv+0rTM0CAsiRIOn35EHoAoYhQG5WgSG+IN/A1UElFoHzNTnhcVDkbqMn2uDFHuEOjFoWlHFRgLckD6tsIe33k8nh3XAstJ3/Bzlb8ckYohch2ypLp1hJDls+eqbdOx22UrcGDDHPBT8b/hL/y/TpZBYcfHtddRNMLZqhWB7wpa/TKCsd0s//3kSLHbyDnpTl8rpaFYweQtKjD8e+r/Q61oTV+vC3g2/3l0+wtsO/PrbQQJB2qTRrFYeHni7lK9tU2oSo3CtjqhRYPGKjZiCoTS2GJJvxgpx2Wl1pYK3ZkQSO5VcSass63S5PfuE4xSGoKODWn6KVQ94BqR2YU8RSbRVFkogNs5INq8RYaLFRJTemoiyAfX1OJDsUJDNqPPCBpTdtez7ck/zRGLi3jvXPUJOT/WRVQ/bXhpiYXrOoRhWT7abvcufRawTiexbl0hxlqPJEnp9c7aIXUxpJRUa02giTEGY8rGRNiCerNBEmdrHxBSypFItNuN8H2X5rU7tI5P6PeOqOYtBJB4Ndy8jwD8vENeVAfdTMvtF0YQ2XBKVyEkZEbiyPmXoJYl8XAHqYaan7NdjTjoBkhh6SbwM5Vvz5EKgKqfY9PVUSSfmP6Kks2eCaiqseZmq9jjp+I/4P9q/+LUcnZECma0FpFmu5Zx0NEc9R12min7J5K9lub6puHp0fRF+ORIcWM7H5mAfU1+i+tycbOvIbaDmANdI8jHHhUt/zq3dgsWpeaEEHTCGzQ688Ri37vL7q0AR046LkLf36IRrwlzYBFaQ74gpVMU01PvLMWGG6A1Ns8xVk6TCiC9fR9mIg6hjqcidGWPDw9cD2sM3doOKk8QRUZhBCd6B6EmhbUCz8s4sTWkAJccncfotDvS2ljlICaOweiAKDVEaWd0/hxHD54nPo6jEUIgpURrNSIbl0UGXlRicYWL4Spi8ZmBpdOJRn74C5ew5w89XiQVMnwoWWvpdM7WIfUsMwcp5WCschroex55VqwcLwhcXNdZ2BclrFbpOyGtA0GTExwKIq9JmJygTYYyGUWhsUpjEbSKGnJmpioFZMZB2WThLNJTGZnRaFmSr1e2ehx0PbaqBW+qH3DLmS8ZhTIaciw22WR1SWQkKoQsJhae6c1yBbaLp/yM95f8YfwV7IRk6aCr2a7ldJLpW8wiEcJiraAaSvYHDurLOGieldfnBsf8vPqTlfsOA6JQvU1w8v3xZ3deRYrl4ZqtDQEzXlmRt8nOrXCqYdwQN4MWj3mNG/GPp79wPbLGNYRWWKVAqtLWvRPj9Q9xks44UjF5Y1mL6PcQnkfqVNFFjAnr5MJBC0NebWDq81qQQOW00gpNtUBgLSWF8NASwEMBYdEhUmPR7/Ayl6L8R4oi1RXQFZQAXeQ4RR8x0bBtVrS5yO56c7NBmmYlia+GaK0xpmxPnqbj9uTnwYtNLD5bL8ePE5818eZLSyySJF/6MB/j/Lbc56kKkbJ09tRaYYw5V5TicrQd88frOGXaI8+Lub4ok2OGnsRuXic96uHajLa3gZ+0kFh0FmG1Qz936FJBquUlo3HhEur5EkA5Q/Q8bbi72eNVPuC2frry6GJVhSUh/yHUChOlpjkitg38mYZdt+UTfqn5Hb5x8qUpcrGohKyXKm40Mx4fa076mju7GR/tCQ47kltbGY8Op9fZb0nu7KT8zez3BlGQ9VC1KgwIy379c7y6sToH1PAz9iu3afQeAlBIB3XzJq5crHcRQnArbPNYfY6N/kMyr07VyznY/RLV2jTz6hUe6a0GfSXIj9pcyz5EnBwi2seINC6JhrXYNCFzQpys1ACR5kgist17FFs3lu6769ilBRiOTaYqfYK0Q+Q0QAgKC75afl4KC0a5JFKDU0dYg8LiutVTvQKSJCWbKK/VWuE4zlR78jyfTKFkp+oY+nGIN8+jsRCDcvArnA/FVcTi5cG4suP59/uYTHtEUUK1ulz1vmbkM407teaCwyzJjo9ScoWfx/SYlcChU7mG7j3CtSndYId6tIeb9cj8GoGIG6f3EgAAIABJREFU6Nlw5VlV0i5Nifg6J86dsvrCWt6sfMRO8mTBVqZR9QvWuDbTEB36hAv1FgJo2xq+mE61NGQH1CG/2Pgr/nXrbYbn4qgruLFRcNSbftl2U43vWOJMYIUcmGYJ0kIhhJkzy3ldvsNtuf74htitp5TeqYLm3W1Y0MlzFraxBQNi0b3xBXbU+qoo13cQzTtUtGAvfIV6MD9OW21QUeUvLRpV+kd1wh0Pu3OzvOB6bUSvQxwbvLxPLh3wQwrXJ9m4Sew0qa3QvvgkJEybrA0hgVS6uKYkSNpmOEVMpgMKI3HXPP0m259bIUE5iBV+J9PrTV/deV6mHMftycWIbPi+S60WMtkxdNiifPYl/3FELFZFca/wfPBZyz69tMTi9I3ILr9kdBLjao9ilPa4SEXKxYy5Zm3Mx46evd7y1pmLxqw1N2hnKWG6z5F/nUp8hDIZJjdIR7HFESdmg1wu1uQLAUnu4CyZNStZYK2lRhtXrX9xAgROQcvWaSwo1ZwcuCMbhGbxy0wW+cIi7W6q+Fz1MQWCf9v6IkNycdIFKS1mgiykuWB3w/LhHvQSxWs3Le88gnYkubNT8OHeeNmf3HjEL1z7gNajJg27uPPs3HHqgkfhTeJwi9fD052bZpBSSIfW5htcD9aTin3nFptuj1gGZNWNhS/pZ2mTSnN8oykl2VfXuMegakUIqDZ47L+Ov12jv+DCbbehtorkCEEmXLwlkabZvjhB1ibTwamiP8ZML6NXmWFM7dL6l7+1dkQi+oPDk1JMRDUCHEcPUi1jsjFJdp4HrjQWnww+a5beVz4WK/A8+31IKahUfMLQp9+P6fXi0ezkYhUlF1dna62o10McR9Hp9Inj07gSzo9Z294lEQFkOUf+LQBUVhIFKSxNjlf2b3C1oZvMP8ythV6i8YsuHglCChKx3FdgEj29uL/DJFa9dDbMPsWCFIdXlMTrfviIn298DzGIz0eZpLlgJr/fEtSDcpxOogjc8rfvxM7oJf16bZ//4HaplTgWG2v3exLdcJebd053TqDUoBxd/zK7jXVmUaWoc9vrEssQVa9zZBr4M+QuLjS6Mk8ag4ZLZMbmYidFFb253MWyWrFE+er5jy/ipap6bXMyOR7Py3tEscVRq4mFnIlMCCFR6nTzsPPqsoyxJElKt9vn+LjN3t4RR0ctkiRFKUmtVqFerwy8bKqjtOll4iLE4ioVcn4URnyif5eNlzZicRpctGR02bpl2mMYCbicao/LgLUW33cHaY9kKke8br1FhyqEwNu6CYeP6AbbxEmIn7WJbFD2AhGWhj3ihM05J8vRtoWkmKhGTAvJSeRz13+KL8ekpCtqeHb9ufRdYHnwBYCmbJEWDu6C+lRNwYFtsiWmtRqb4pio2MZThvvhQ2qqz+8ff5nEuuy3FRXfEE80RtPKUvMMvUSS5oJbO5Z3Hgn6CdzagfikxW/c+/ZIWOhW3DmB5Spku3cJnNM5agLkaJxbtxDHbZal/gyC4+AO27pNgkcRNogI2Pa6zBLLfbtJY8EEXynBvtjlLg+JjUNc28Fb5rY1WH4vrXNPL9fGSAGRCKnY9S65AqibFobFnipD2JmmZM4poxVwubP+ojAURUIcl4S8UglG+gzXdahUAqSc1GtkA3+N86UzriIWnwxe9FN+//7914H/HvgL4DZw+ODBg/9u2fJXxGIFLh45mP7McRRBMEx7nL6h2dnHPfs+u24Zgs2y03VvPS20F5A6PhQ5J5VbXO/8iN4gHQJl5KJuj+mKBikesy8ozzG0E48NP6EwBvKC14N9lJjJPTuKNQaKANTclF4/pCIWh9fbRYVj5xp5GOLZBIocmef4eZutoiz1LAxzsT4pLK3YZbdSkpub3hH/8fYf8/8ef4WTvIqrcuJc4ipDHGW8d1ge562NiKqv6MQOm9Wco64k7UX8p69+C3dCX7Jdy4naLoFYHz06yOvcvd+k88EhNX064npYfYVmpeAgustO/MHi7Xp32NFtDIIT/wZNN6VvHYScJqAHaY3GisCQ3/CITxz23VtUvfXXar0mSFM5KjMGKJCD6wWEsBTKIS4Mro3nbNm1SSmERg0s7BvmhGNbWdHrQ84RC60XE9/F6z9fH4uiKOj346nPHEfjOBrf96jVKgghRhUoZyl5vXLe/GTwKUiFbAL/64MHD/5PgPv373/v/v37//eDBw8WuvVdEYsVuCy9wukEkIvXP+tNftZ9HruODnO+Zy+DW+fZ4W9epzh4TN9t0HG2UFmCdcbiVC0MrkjxSEmtSzJDMHynQBUxVfroBSZPAI62RIlPsK5dpxC05QaVidbpFvjQ3sHUN6g2HEIhaEeaqjt5Ips8at8gPHlIwyyePcuZnhZ1HfEfbf0x3zj5Eh91drneSPloz06ZYe21NeI4RzsF965L3nDf4+tb786JVqUUPKWc6a9Dq3mPG1ry2GxRY33Uoq02aAwm8H7TJ3+q0TOCz319kx2nBQieOXfZ8FOOijpNdzr8YyzYIFypH1Za8mP9BjdqpyM9jgNP2w3uVo5p5wGZV8U47tw11zcChxRpchyToosEt4iQ1kwRC2kNXtYjWeIEOyvX1nq+C/AnhUXiykUlr1LKEdmoVEq9hjF2imgsikie33nzxTg/n1a86FzuwYMH35z5SLJCCv/SEovTiTcvrleYTnusicFPjX3eXO3p9zkIPFxXE0UJaZoTBN6FbMyXQSqN41cgK+hUrrHVfo9kkA4ZwuQWxwFfJHg2Gbgilh0qrbQEds25E4K+rBGY9S8r7alRu/DI+uzV3yBsTusBKm5GbiR64gUf1h2ovcJhK0G0jrjhTrcS3RRHGNOYKmN2ZcFfq7/DV9SH/OBklwf9XSZvu6wQbNckqn/Iz+kH7OwsFypaP1wblfkgu86Nm6W2wt2oQ281sbAI8uY1vIFfhavhqPIKu72xbXdbNml6MQjBE3kLPxAYK+Z0FQBHdgNvjUf2ceSSezWMjZc6Xs4i0z4fmJtUa2Wn20U0VgpTXjfaIcUhpULPWJTJkHlCbsvOsdLm+GmHxJmPWgghS5v6CTh6ren3x4bTTjaMMSRJSpKMI1xKKVxXj0rHtdbkeTFFNq5SIZ8MPk3lpvfv3/9PgH/x4MGDHyxb5qUlFqfBRdwznUGoXyk55/twytGXekqsXOsUi5eq87LXwWW4jp4mSuLVN3EOD8iUS8/bRE6kQwB8EZHbACHKbakJcwIhBP3UI1zTpfS06ZCGmxBHHh3ZoLh2m9Cd/42VEhxHATvBDCkXgrDp86H4HLb1Y25OuHy6IudZ4rMVTJObDd0lklV+dud9fnLzId893CG3El/leKqAouBLt+f7e8xiq2kxT5fbTxdW4Nwaez40m4q8Nx99mMR+cI+GNx2lqjckj7NXuZm+R4KH9D20THikXyHza2zKA07sBnXVnVovtRoVrE4ZGAsdU8f1FMdxyNYpKlAetSvoaoXcFCCWE8zypTh9zwgpMNLFaJfYNIilwVqLsgXWSmC1QFvr+cjIKrzIBlZFURBFBVE0vkmGUY1SrxEipaTZrJGmY7JxVX76/PFp4XL379//ZeCXgf9y1XJXxGIFzpMKmUx7WGvp95Nzeu+feZVT7VsY+iMr7lmB1/kjNOu9M4QQVKpVjrsJUbBJGB0waWOphSU2cq4z6BAZLutYg6MtSeKt7VYppOCj4E2a2xq14niLFce04WfI5j3e+9DnVT2OChSZgWBmPGC/63G7nuOrnK/uTntSFAaSWJUkYwV8x/I4aXLbX1x2+q59hdvN8S2tteDYucbOkrbokaxQqc+LEoUUbO26PGm9SVGAdiQtPyRzqmxzQGxcwgVul/tmk9qaIoVH7TpupVyoU1TYWuFRYSx81GkQ1srUmBVqLoo0t+9CkluBopi7d9XAL0QKMEKDtaTWQwmBEgZhC4yZXs9xTq+tKMf/OMpBL297symRa9e26Hb7g6iGT72uB8tNp1Bmn2kvSqro04pzam0/Vty/f/8/BH4R+G3gxv379+89ePDgjxYte0UsVuCsL9qhyVUcp/R6EfV65QKW4Jfb1GeYkllkxX1RnJaAeX6AjjIKa0mcGqGNplZUyywUAb2EcExBCHqyhmdWE4v37V3SRh3Eal+IjTAlzadFg0PUvIy9pEbzlev86KHPG7wLUDbnsv7cCVErogZKwtO0xu1gvU9FVzUY2WpOoFd47Lw6b3udB3VYQiyOg1tsqeUXZ17doFkp9/skDVF5SiEkj8WtgVGUZdc8I5AJ7TygurrQgk7soIJxCawbaFqxS8OfF6RmheBxf4OwNiY+Qggi41OTi8mItcNYhSQxEkfmUyLf2XtRCouyOYVxMEgQEmsdJGVUyHNAirNFLMsxnmfE4vltf3h+xnqNMjqk1FivMWtR/qd/+k2klLzyyuv4/ukrZ86Cb37zT/jGN36fjY0NhBD8vb/3nz+XcT5JvOi9Qu7fv//XgP8N+DPg94EK8D8BV8RiFuteiKd9uQ9zlkVRDFILs34UH2+3wEnh56QB17qUzPlTP6d3+2xUKxx1uhROQJxZfDEmAa6NyAgWbkkre6p0iNWaBSaMI7xb3ENvNHCtJcklnl5OWKQUHMYB1yuLNUpxIiAUNO5s8MPH9/l88YCK6HOU1ql70+Ttmt8hMx6OXHz+rTzdrVhtOCya5D8KXue2P//bBRWNaYlR2eoQ++IaW3XDst8tMm7pVArkVoI1SCwfum8QBIzWOyjuUOnvkeiQypJjg/Jea9saaiqPIzjOqjT8o7llH/c3CKsLPEyE4iip0HR7I3v3fu7y4UmVo7g6dTxpZglUws16n1c2u2ALBIbCljbfQoAmx6AG2opyPWNBSYGrz/54fJFTIefddlnymk752ZSuoZrvfOfb/Mt/+S/44IMPePXV1/nCF77IW299kV/+5V/DWye2OQXiOOYf/+P/gX/+z/93XNflH/7D/5o/+7M/5atf/ekLb/tFwoveqX5Q/bFm6jDGS00s1uE0Jldh6COlWFjtcdGow0XcN6UU+H7Zbv20lSjnHfMsKSPHUSjlUBQZfVnDsdmoDbgapEOWhbozHNalQ1zHkqaLPSjeNa+gN8omUkII2onPjl6d4xcr1IVlRUR5CzVv1vjhozf4vPkRaS5g5pnqSEMifZwlJho7tRSbrD+P1zcs7bZHXY/Pw0f5LrffWGwB77rwTN7ghn08+sxYgdhowor2611Zp6HKF0krDcqWHvUtRKGYbM4hleSRvM2W7rCK0R3GFZQzTxR04NFLFJUJncdHnfpUpGJuHS3pFiEYw0kU8PDEx8rplIUxljyHbuGxXYuohOX5KQYdfYuioMhTEBaXhNS6DFNzSgqqvj7nvXu+icSpt/4JEItFGFqU/+Zv/ha/+Zu/RRynvPPOu3z/+9/lT//0j7l//y1effW1C+/Td7/7ba5fv4Hrlr/vl770Zf7oj/7gs0csPgWpkLPgiliswKoX5ji1kE0pry9v7PP3/BACqtXwzO3WLzLmaVCWsRnqocNxJ0Orgv10m+tq3Apc2lXpkFM89AbVIe5MSei75hV0c7ozZWLXh243wpReoqm486mMupex1/dpDmyzm7ca/PDh59hM96Eyf2uJVakeYUl0iF+sETMKwdN8k7oudRpxofHv3VnJSPJqEzpjYvHEuct2sHxfniUNNhrlNd3JfIQtsNUNOqk3imIMURjIhcdeqgmdZwuFpWmhSFW4pJJD8LRX5XWvbMN+0A8JaqsdQ/NCkBuPv3oYctyxbNQV7owUIk5KUv/GdpdrjfE+KykJA58g8Dg56WCMoTAGZUpzEq0kSp6/odZ5U5+n3/6LQSxmEQQBX/7yT/LlL//kpe7T8fERYTgmzZVKlR/+8MGljvEi4EWPWJwVV5beKzEfcXAcTb1eGVV7rCIVF3fuPNs6SilqtRAQ9PvRKa24LzZmud7q4zTGYozBmIEiXwqE8su5ndB0zDjC5hItfTBrZYmK9eFVOyO4+0jcnSMVANWqJEpXqw2FFLTS5S+6OJk+7ubtJkdqi6RYZPu9mjQs65syt0/B+EH7MPw8lcrq23ijKenb8hgSXGqbywWJqVH4wXh71lgit4mRGt+Zj3od9PzyZew4POo2574H2IvrK1NsTiUgyQVHPYfMnU5nzCLOFanRvLfncdSCOIanezm9/njfkrRM6e1WYt6+PR/hmnz5SylxtMZ3XXxXo5W8YJTx05sKkVK+cKWmGxub9Pvj+6bX67KxcTZ7+08DiuKT/btsvNTEYt09NDmDl1JQrQYEgTvq7XGaRkMfR88PIQRh6FGt+sRxSlEUF5g1XW7EwhiLtQZrDWIiz78RSnKjcFXGXrFNPgieKSxxsTySkLJepa+UJR+EtZ+o25ja4heeEIKDaH0/jXpYLFVtb3j9uXPdvLNB19ueW1bbjFQsJw/ilOf++ragsIJH5ho3767vgiul4MC5CcC+dw9vRZxyL98gcMsnzbNeha6o4vqaXuoy25YiSiXKGW+scCr00unfrp14aG91ZEhryYcndXqqiV5h791PHYxVHLQ1jw4USTrQMiE4ODI83cvp9gydbsG9Zo9f+HwfORN9uIju6TT4eIjF89v2ecyxnmek8+23f4KnT5+QpuUk6Tvf+Uu+/vVfeC5jfZKw9pP9u2xcpUJWYDiDP29FxcWcO+E0OkrXdQgClzQdW3F7ax7ky8c8X9O1RSSofEDZQbfW+StXSkHouyRJBAgeJte55z4sx1+RcFSnqA4RUhCpOn0C0sp8pcTUsqfoAeE5hscHHnc25me/NTfnUSdkpz5xXQhB7Dc5jAVb+bOp5TOrllIjT6SkwsVd0ZgNIPDgsdnFu3Pr1BeY2whpH9bZWjHZaxUVdmsJIMiKskeLCHziTFLxMmZfHq3Ex51wJxVCsJ/Uqbhjb492UVtJFoY4yJrcFsvTdr1UI6WkG8GPHrlEcTF3zSWppdvL+MKdnK+9njI5b7LWTtzP3qk1R2fF80+FPM+qkBfPHMv3fX7nd/4b/sk/+R9pNjd4/fU3PnP6Cvh0lJueBVfEYgWcwWzsvCZXFxNvWlYFlMZW3Mx5Ulxk3PPu7uR6w9SHEKuJSj2QPEkcXJGRSI9H2TVuOc+oiD6FXewC6ihLlLkEcvXL90hvg7s+GlGrCFqRQyNYTRilWv5bzLbmBvBVRjfcQfYNG/n+6HPXxMt/ViFIVQU3X5/COtr4PG9UT6+fqVcFe/lr3JDL+8Ak0iMQpV5kLwrpOxs0pKWbKmozVuonfQfXXZBGcnyiTBM4OftRiF60zAyOuxrX9zjoCm5vzotb01wihCRKBd9+z6EfzZMKAEcZfuXthLduz/8eQghcV1OtVkjTlCiKR14zQ1xGd+HnGQ153ngRiQXA1772s3ztaz/7Se/Gc8Xz6Bt1NlxuxOmKWCzAZLXHRU2u5Gk9i+fWXf5wG1txp1P9ASbHPW/k4TwX2PDUDMWZZ4l8NEOHokhJco9YVHmcWW65e/QKh0Avftmn1iVYUoFgLTxKd+lTY8N255qVzUEITlJ/LbEwQvK9pzUCp6DmFzjKUnVTlIRrYY9eXpkqXR2+X7qV64iepZkfAOCZPqmsLnXDtKfwTXjm3MG93oBT9AEZYi+pE9erUPx44fcHRXPkWdFNXbq2xkbVcthz2ahOv6iNgcS4OAs4gxCCvajOTXlMIiprHzBZAVHuIiQY6dCOMuoTbeazQpAZTWEl335HEcWLzJgsX7yd8de/kC6N8lUqAa7r0u32RoZQQkynSaQcRjaGBIOJf5+WbLyY4srnuf3yPL7UWfUL46oq5DOO2bRHaXJ13hv6/LnHReRgbMW9zpPifDOu8xKSojCls2bFJ8/zwd/pQs2BK3C0ROU5BZpI1HicQqiWWzerJdUhxgo+Sm6QyhABdBKXZrDe47ta1aSFwJ3Zbjt26OQhiXXxaw6ZNWw0DRmQASdJgeh2uFPrYJEwU/XhkpELj3Z4A/rQzA8QlDqRZcTCEykGiVxSQXLkXCOvbxIKQaflUXPWH19hBUnQxPMVTw82ue5MV8xkRk5VVTxL6rhVl34K9TBn9hre7/o43vIXiXUCHvUsfrj+ZdOJXcSIDQhO4gBX9/AdQ2Egzsuyzx98pOnGiy5Oy0++kvHzby4mmlorqtUKeV5wctJeex/Pko1hCmUYhShfAHYp0XieGojn3Xn0qrPpJ4erVMhnCJP30PClnefTL+3z6g7G6148YjEZQen11ntSnP/ZcHYiNBRnHh+3cRyN1hrfd1FKkedlt9Tyv8vbNt/aCYmfxHTz8nLsixpFDr7TXZoOiTMHX46jDJnVPEyvk8tx+iMzmtM0D9FasHcScrtRpglKK+kmTiVAOILhFpt1yeN9w82d8v9dT4HX5JmpEtjuHDFzRUpmXYQUdCo3yGKf7eQh0uZLT7MUEKkqlaI9911Hb9KvXR9dF6lTPdXxPUk2cTfL8EJS3aaIj6ciOYdmg02nPJf7UYXIqbHjZnQSB3/GU6QTSbS7+rGR5JJ+WuFGuDoK1I0lyaxQV0j2ulWafp+skAip2G8pnh3Ok15jDP/+V+Brb/kIEQy8FcprLc8LfN8jCDy63f7CyN5pUBINGIu410U1Pr0aiLIl+2fsDfcpwWeNz73UxALWv7Q/7pLRWZzHL+O8+3yW/Z0VZxpjp7opCgFaD4mGR7UaYq0dPfTLToql34Yxlpqf0OuYUSogkTU+6IVseW1qzryWILEePhm5lRxkm3RsHWbCsUJKskLgnML/Qg4Er91Ec2w2cCqLRZ21qiRODf7EDN9KTZ8m/SJnQ7VGLpelEHVwUoUgDjZ5qjy2ow8xSiOX5OJzMS/v7Kk6rfrtKcOuXPuscAoHSp8LUR+X8zq+4mHvJvcG/U16hUdjQABaqc+R3GYjzDnqumzU5j0rupmP562+SA67DtYKCpOxTJqSF9BNvMUXnBA861bITdkk7MGPE5LU4roKx5GlhqfI+ZUvpXzuuuX4uHwplsRWEYYBelDCkqYZUkqUUhSXVFc3G9WA8n4YmtJF0fh6vUxr/hc1FTJc9wrnR1F80sziSmNxaXBdNSrRXFbt8XGVjM5CSoHWCmstnU7/TOKe01aULFiT01xgpxFnWjtucBQNshpKSbTWg+iQP5oh5XnGbkNz3C+IzXjHU+vyONrFSxK2vRahjjFWYhEUSPayTdqmgRVq4W4LIeimHhvBepFjJZC8c9DArQboBd1Oh/A8yf6R5camnTvHBZr9bJMt5xg9cLWUNsdO1IHkboVn4jWqyRE1OgvHcMSYLRgkR/4t4nBjImVQQjqKJHPwxPLZ+L7dwtXT6zlbdd47VtwVH9GmxpZM2Y+rPLHXcbUhzaBRnU+BnPQ9PG+1GLPVkxS2fKwcdhx2G4v3rR055e+2AIUpiQcClElp+DleDTwnpxbCa9cKXrsxzUmstQMSIVBK0utFZFk2ut5KF1o5FUXL8/zSRHNB4FGpBPT7MWmaDYShME6hXI4w9PlWnFylQj4pfNZO+0tNLNZrFS5aMnr2h8jQk0JrhTH2TM6ZEyNzHouSdcd6HnHmJIrCIKXBcTRpmtHvx6MGR2EY8NoNw189zEfnzFMFUSZJjMejaHd2b3FVsXRGPERu1lclADw+culbn+tqfVRoZ1MRF+CJYiqloGTZOvwg22JLH+PInEAm9Kwznbd3PPbEXdpFj0Z+SNVOEwxXFkQiJFU+3eoN0M5iuicEXVHD42jRt+z3A5zNYOF33kaFH7XfKNvDZy7WcxAJuKrgWb+CiCQCy06lT+AaWn2NWGDJPQljoBWPl+nE7kJi0U8EceEuvYaSDBAS3zH80usR4osrhwXK+6ZWK/VQrVZnFNIvisVRNM9zB1E0RiRjSDjOAiEE1WqIUmpq3LOnUNbfUM8zzVJu/4pYfFL45CMWl4uXmlgYA3JF4yT4eFMhnufg+y5JktHvJ9Tr682PLmPcdVjnSXEaDB/AWiu63f5ImW+MGav0Ad9xSPLxw3h5FEVQGIla0UIbyjLRdc3GHh+7FLqCpwV7JwXXNk4TMhc8a/sURuDpAl8btLJ4OiezDvt5SS48mSKMgZnZuatyElll361ylCeEeYvS9FthhCLXCidYT4oyFcCS3e35mwRLqpKMhVRWCAOBCxx1ytLLx90m/oQwcz/ShEkfqxzUmmjWQUcz7LcBZWvyk56iWZnewW7qLb2nkgwsJan5yu3FGptZuK5DtRoSxwn9/nIiPhlFG0JKOWqoVam4aF2mTIYpuzzPl+oOym6fZflqp7O8jHeI0wpDV63/Yoo3r9IgF0XxiZebXi5eamJxGlzUi+I06w49Kcq0RzRIM8D5K0ouL687FGfC+UWsnudSqQTEcbL2AXy3kfGjA2906EoZzJKog7GnK//rph6eXlxlstfxKVTAcEClHaI4J/Dnt50XkBaaJJc8OfbIBrbdxhhO2oZaCNWK5PZGj9CVHOYbbOkjPJGQMB4DyoZriREoYSm0R0dPR2SMsTisj1ZJR5Hk8+mQH3c2qVxb7lL6rOXSqJX704vLY4uKytxxCyH5qFXjeiNFreA5aQZRpueukeOeR7MytmQ+7KhRqmQWxpTlp0LAtVpG3V9NGoWASiXEcTTtdvdcplfGGNLUTIk7tVZorXFdZ5SymxWGBoGP502Xr54V66Ia5f5NRzWed8Tik/dTeDmxokXSpxJXxGINLupFsYocCFHmZh1HE0UJaZpPrHu5UYfTohx3qA6/WJRCKUm1WvYuabW6pxLPuRo2w5zDfvmScqUhKtTCc2ERxKnAd1fvn0ENolPTnx/3fRI7/cKXSvLsWHH3WjH1u/cSgcWhkyj2TpzROklS0OoUSKlotS0Ww/umhqNybjVjLJtsqSNymLPEXpVYlZJTRWSEFHREE4+xCVe/8PC3akvXSTJBONFi/ahdNhKrhPMn+ahTVmY8bcGd7XRhkzGAp8cOYkH8MeCiAAAgAElEQVReKkfTiSS1oCwfTY279JaIs3JGr4Th7Zur+6qU0YKQNM05Pp6voLkIhp0747isuFkkDC2jHxlKlSnL5yUMHZKN8lnhTxGgy5xADMe+SoV8MrhKhbxkeF6pENfVBIFHmua0271LFe9c3PGTUzlnrkIw6CDZ78ejB/RpcaNe0Io1xUCEWhKbxTuSFhJ/WS5gACkl7cSb8rQ46PpEZppUDFFv+DzcT9iq54S+oBNrpJIcdx2OuuNbptfL6UUWKQeMQQparQLPs2Ro3j+sslVJEPUNqrI3N5YjMwzLdAuCqNBU1ziMAhSuN2q5bi20vB2UXi4+Oey6NOvlvjw7EsS5R6Mx/yg46siRwFJIzbOjnBtb80Rn/0SAWn4ch12PWhCx33ZBLg57pHlJFAHe2IlZsfuEYXDhaMFZMBaGSpSSdLt98jz/2IShZaqnQpIkxHGyQBha/vuiROMiBllXuBg+a4TupScW6yMDlzsrkFIShmWOedaKe9m+nfWaO2+0wxhLmubU6xWMMROh3+V55lloXc4ki6I0JDrvw/WVjYQfH7lYBFoW5Gbxpark6Y43tQ5Dz4e9znykYhbVmke/cDk5MUiliLqSTlS+FLPM0GpnWNRc106hFEdHKdvbZbOxw55Hmktub0BNxugJTY8jLd18eTlsYU8nPJVa0U1q1OhwJLaQ7nKRZauvRimQLAcjXRqN+eVPuqXeYxKpcYmTGH+ij1qcQC/zVlYhZdbhuBNjhF54xq0t9wUBgTbcvwl5LueuubJ7b2V0bX1cD+NSGBoihBy1WofnLwyFsWNop9Mbrf88hKHD7X7WXnCfFlxFLF4yXLRz3zC1YK0lCFxc9yzNzIZjn/WiO9s+T4ozu91SA6FUKWibLA0dPiCHZGMSpfNmgOM49HrnNyQawnfgVj3no5aDqy15uviYpBREmSBckw5RUhJlmm6i15IKKEsee4lCSk23B88OcioVQauVY6xEyMUvSYCskOS5QQ+m3Z3E4U9+4POTr2u2wx56Ir2xqqhFK0tu5NTyyxDpKjpPSYPqym3GuUNt4EMRFw5qpsV8YSzHbUDNPxqElBy0Nbd3xr/9s5azso/KYE1+9Njjzo3FyyVZ6fNhreWrr6Yz11z5QpZS4LouvV50aj+Xy4DjaGq1ykAYulwfdDZh6DiqsYywKyUHJMqcyzEUxvf1cP/WkY3nXXVyheX4rJ32K2KxBhfVOlhrcRw16qh4lmZmk6TkbGOePjy5TJxZFMVU3rj01dCDh2SZZx4+9K0tBZppmnJy0rq0m6QRGLppwXGkyAu7tEtmUUiWlkZM4Ek7xHEUpyIVsUQqwXGr4IOHGVoLjk4KarXlZZJDSCk5OsrY3S2n9k+exCS54g++K/jpL9S4We2MyIIrU3LrLPGJEsSFQ1WuTyVZx+GQazgrQgfd1KVWGZCKTPGs7WMKQ7NWrnPctqSFQs2JQcYo0MRpju/CsyOJWJoCGaPdyeklmk7PUKtM758xtrQzFoKGl1HRMd1u+V3ZOGwsoBRCEAQ+jqNHJPeytA2LUEYLHNrt3rmiDecVhrquQ6USXJhElRqh9VUo1lqklBcgFVepkIvis+Z4ekUs1uCiJldDN75+f70V9+Kxzz7uadY7awlpmSbJph6Srlv6T5QaA4vrukgpRxGNy2hNfauRD2Zb0E3kvAASUKoMpTsrrubjrqIVa6qmIPSWL5cXEKVjUvHhY4OQisKU48Rxju+vv20Kq0jTgsOjjCQvX6ZpLvmr98D9XJWdoIOSFi0tSSFHhlqzMPZ0fiT7cR0hYJvFs+rcyJEzaWEEex2PNC9Ldh/vG4SUOK67KFAxBSElBy3NZi0vvSjW7J4xlnavjDY9PRSEvkVNEMS0ECAkWWb46uemBZvDF2wUxURRSa4mTdZ830dKSVGczjr+tBimXPI8H0QLLrS5KawWhvpoXf4AaZqVQtZLdwyFRSmUMPSn0paXLQy9wmpcpUJeMpz3BvM8F993BiZXq7UUlz12ieXrnbat+Sr4vkcY+kRRQhSVBk9Syol+IZOCtvFs7DwP/dvNHAt0YsWi5IEQgjhTOHr+AWwsHHY0vbScWfdiCNxi4XHnBfQziZSCg6OcR8/m97UoLEVhUGvC/0LA+x/0cf1pFnPckRy0JVAbkQvFwGZyAZSyZEbirEiH7PWrZPhYY0nyBE/Pz677uTuK+DxrezxrTbeUt1mBs7w6dQq51Tw9FisdSoc4PM4Z/maFETzeN9y+Vv5mUWIxKLLMcqfeZygNGZtOySnTKShndtPaBjGKAkxaxw9t489KcIPAIwh8er3+KdOVF8NQGGqMwfNc4rgUaH5cwlAp5chYrN3uLhWGDvf1imw8H3zWUlAvPbFYl+o4ayqknHl4GFNacQ/DnR8nlkUshlEKa825CYVSavTwnhSylds3M/1CxCjHHATlbOy8otC7GzlCuDw6WWxXLiVzJaV5AQcdhzgfX+ZWSI67ls3a9Lh5AVEmkULwdC/j8MRSFHaOQAghiPo51dryt3BRGPaetElSy/auM1eh8e13NfeuF5jrDbaDDq7MiAoPvUDEWaZDXBy52NNivx+SEoyWPUkrXNOtqWW6iYPW5Q/eiTWPjufdOK2V5LkdLbcM1lr2jgxaC7bXEJEkMcSpmLrWerHk/cf2/2/vzcOkKM/1/7uW3qp7hllkGxZXbJZhUxRRNOa4BJck7olHcUEUjKLRGH8a43HLQkzQQBBQVFDcwlGjRk385iQcDQGiHlAWdYARRBAYlpnpfanl90f1W13VXb1WdffAvJ/r8pLpqZ6umu6p93mf5b7R0leBJDOIJxVEQkmMG6MGQ2mxq+JEp4j/jJl0vNEQTzJ87jIXZpZl4PN5wTDI+lxXGkFww+12IRhMT7lUozGUCHzF4wlEItHUa+VrDFUf02trkOdQrHEoZCz8fv/ZAC4B0AFAaWtreyjXsb0+sChE8XK7TEqTgkMkEtduELXyGtFjh3ImoI75ud3FN9Dpb/oE86bQ9O7SbHyQ3AC93iTa9wAyw8DrNgZPLMsglmQhuFS9hK4wj1CcS9mZG0nKDIJRBnUe9XchyWr5AwwDJOLY9HkUTicDl5sHx2WvnizHIh4T4TIpiSTiIvZ8E0yJdzGIhmPw9clWUP1qD4cD3TLGHNeAJncICsOYBhYAAMY8wO2KuRCH8WdL4NEZdaExNVqbkBgQZatoksPm3W6YNsFyDEIRCQ31+SdR9h2UEEsATFJBUx8lr8bLwS4JjEmtJJ5k0L5DRDShPvfKybEMsavyehoImVkNAFomzWxhBtTxaDX7Vo6EfnmQbIGiKOjszN2gaXdjKGAezOQil7aGvhmUYg2lhwuT+f1+AcAiAKPa2trifr//Nb/ff1ZbW9vfzY6ngYUNOJ0OeDxOJBIiuruNuyxrXiPWRbLsUM4kYkTJpJj3BlgMmU2h6Rozr4kPkd0laWRTZcDVG+DEo4F3NjSgKww0eCUILgVyqgdDlhkkRA7dUYemiWAGw7CIJhkkRRl9vDLCMdXY7JimKI7tm8D6z4F9XQoUOQmW5eBwZi+2yaQMl7GagGB3DAcORKFfuEMhEYJPNp2cCEVZrN8KjD3eB4GLwcWbZ5I4lkFUdEJwqAulrDDojAmIyB7TwDOqeCFHeTS5w4hJLvAcg2DMgU++dKKuzgExLoE1kdF0ODiEIxK8gnlwcfBgApGYeh2KwiAQknMGIoGgCClXf4giI5pa848dIGHQEQzq6uqRTNrf00AwW5gdDg4ejxtc6nfhdDrAsulAt5JZC5KZ0fePlEK5jaEMg1QwA0t/y+rHTm2ENgseKaVxCDRvTgLwVVtbG/mw/gvABQBoYFEuueR0iRQ3kJbizvVcK69b7nN5nk3Vicv391BHSHmDv4edkBpz5g3S7XbD51P7E2RZSdWaOfC8iBOPCuOjbV7sD2R/fJ0OY3NgbhiICosd+9R/n35cGC2NIliWxW2Xu/DgMxEkRaBjbxAejwN9GjyGkgbLsQh0RlDfKCAciuPg/ggk2diFD6i/w1BXGPU5lDC7gzL+d3UEZ07yIRRyw+eMw+fMVrgUU5oSwYQbAVGAAnM1UnJtccWN7d0OcCyHpMTis21AOMogFElA8LAQcgQPud7ivR1xRJPG5wTDMvrUsVmfUVFSEAghZ5tPKCyBYdVG3EtOBep8PoRC1keUS4FlGQiCB4mEiK4utUeIZADUhdkDhkFWb4MdQY/PZ02GPBf5GkPJNA05LpFIpBpfS3999XfApv6jZRA76OkZCwD9AIMdcyD1mCm9PrAo5kZhJlTl8bjgdGZLcZs822I5o/TnyrKCSCQOt9upiVWRHUuxO7G0v0fCdsnkfKgCYh6wrOpSKYpSRlOoEyf24bCjU8HeruzfTTzBQPAU1vFQFBnhKINmr4xTjo2gzi3rGlJjOG8i8PZqwOnkEOyOIRSIwVfvhuB1AooCjpEQDCUR6I5DNAko9ERjCoSkCD5jbEVMSti/JwhZBj5YHcbkiV50Rb0IxDzwOuNwcSJkMJBkBpIEhJNOSCiuw1KSAVFxIiky2NmhIJzqP0iKLIIhBWBECJ7sP3+Hg0M8Lmn26LG4hH37RUjIDkQkmUE0KkEQjD9n/0ERucZFEnFRs38/ZzwDj5uznAUrFVIGyAxmyMJMhNTIiLU+m1ZKuSGTSk6bmKEP2r1eDziOQzgc0QKOdGOovtE1f2OoMaig2MUh0GPRAUC/O6pPPWZKrw8siiGdOVBSvQEuJJPFSXFbuXmUOm6qb86MxSTEUuVifYrU6/Vo9WWzrnmWVf09VPvp4vw97MI4aZKudWc3hQLf9vNY86UH2/cZdSkYBohEAcHcLRwAIIoyPLyE00ZF0OSVU7VuH1RPE3UKYdIoBuvbZezoUFPmyaSEYHcMwW5jDZ5hAHe++dXUQQf3hdCvpSF9TZKEgx1BkBhv774k/vVhGBNO8IHhWIQSHoQyfgwvS3A5Ci9kosQgLrJgwKDZE8XaDhYKy2spa1lhsLcjCZdTxBFNPJwu420gnlDgcCjo2JdANMmCYXL3XRzoliHo2jy6AyJEyXzRURQF8aTalzGgicHYo5IIBEovA5RLsT0NBLMRa/K3ZCbilW/yiXy2q5+ZUa9Zlo1CW8U2hm7Z0o7m5mZ4PG4oCslQ0KDCbg6BUshqAEf6/X5XqhxyGoAFuQ5m8v1x7dsX7PFhlFWYdG9bTnw+D+LxJFwuBxiGQSQSK/qD4HI5wLJsWXXUYp9banOmPgPgcPBgWVZrYuN5rix/DyuoZmVeAApCoUhJf2Q7Djiw9isBSdl4s2NZBS6nMSpTFAWyJOOEIWEMaVYDJjJeaHbNsbiC2S9KSEgMIiHzZlVFkeHxFp78UWQFjc1uuDxOJOJJ7NsdNK1N+wQWZ0xugNNhKn4NwSnlfY9FCUiIHOpcMob3i4DngFAUWLaCR1JJ25WrwZoMlmXgcipwuVSjNp5VEI6mxLvchcWvAKB/owKP4EAyKWPvfjlnY1AolFT1Mnjgtu8BfXy8pdHQUiAZOLs/2/pyA1mgyeQTuR61rMIgGAxXddqE9HGUes2kMZTnOdx888349NNPMHjwEIwaNRojR7Zi9OixGDJkaAXPvPb07VtX1RrP9F/ur+la+/R9RxS8Xr/ffw6AywDsA5DMNxVCA4siAov6eq8qHR2Nlzzb7nSqN5tIpPRuc7VxkUUkkvumoG/OLBeHg0st7OrPUx0b02OhlWxkI2npSCSKWKw8lUFFATbsdGHzXnfGFIgCt0v9zcTjAAsF352QQJ1LvR5BUMdmQ6FIzuv7ZHMSy9/nkIxEs4IXQlFZCwBQRDQe4csZVBA8bganT+pj3gehKBBcounaLcmAIjM4rm8MfTIsx0UZeP7/cQhJ6SAoGk1meZ0QZFlGXX2RwhaSiKOGutGxL46EZJ4ETSYlxBNqBu7csXGMHKIGEPrRUIeD00ZD9VNCVsokek2MYDBclZ2hOvnEwel0an0N+sDJDhGvQqT7OMKWso6KAiQSIrZs2YpNmzbgs882YseO7Zg/fzEEIXva6XCh2oHFtIc6arrWPvtAP1uvlwYWeQILoobHMEAsFkc8Xt6suNPJIxwuJ7DIHZTYMULKMOoIqerBEMmZ8uV51cJcf7O3urPkeTWYkSQJ4XDEFsEfRQHW73ShI+AAzyrgWAVOXobXKaPRK2NwkwKPh4fL5UoJAaXHYfPtlt9ZmcC/PuMQ7IqAM5H35BgZDk/hrEUynoSYSGaJZmWSiMbA88DUy/oiLKYt2gkMJHic6QkSRQFiSRZ1bhan+RldT036mlwuJxjOiUdfigEONXOhz1qY4XAycJpMxJgiJsC7zK9LDd5EsByLoUeIuOSU3IGyPjVPMgHlZjXImHIikUCYNJlUCWIeFgqFIYqS1hiqXhunffb0E1B2oHqM+CCKIsLhiIVSrNKrSx/VDiyue9BEja+KLH2wv63X2+t7LMz+8BiGgSCoUwiRSAxOJw9FqcVkh3lW2Q7lTLXfQkAymTQ1OcrsMNfPzas7wPJ3ll4vsb22t97MMMDYIXGQ5rtMOI6Dy+WELMsIBIIA0mlst5tcU7Y89AWTnRClBNZ8xsNM5kBSWDDxBBx5AoZYJIaujgAYBmge4ARjspgrioJIOAafG7h3mg8NdTEkxBja93twMMprnyMFHCJxBh6nhKTEIClxOEIQ4e8fRiBgbHTlOE57XyKRGM4YLeF/PonD6Xap2Qolt+pnIiYVFViEQwkEuuMYNNhpGqREImpQ4WAlfHdC/pS8XrOhkOBVvobDalurE3KZh2XruZR+TYUg5R6rHiN06qP6yD2/x6Iken1gkYnL5YDb7UQ8ntSyDA4HbzE4sCcosUM5k2UZeL3qIqq3Yi5E5ty8fmepSikXtlq3Uw+jVEjJxXjTVVJNochxTYK2s7ziXCckOYh/rktAYbL/bCRRBp8jiAx3h9F9MAgGDBQFCHQG0ae53nCMoiiIhmJwcDLuua5OMwZz8sCIAVHIMrCz24mEyMLByXBwChycjHq3BH3vpb7RldTYE4kkJEmG0+nAf5zkBsPFsGJdHKzTBaeLQzIpm39GGcbg0mpGNJJE18EYAAadB6Jo7mtMjycSkqopoiiYMj6W188lF9ky3sb3iefTMt6SpGqfFOsKaifpPo7CZb381+RMXZNeXTN3VoNhAJ/PC47jsiTQS4VOfdQGuyTaewo0sEjBcaoUt6KoUtzZhjzl/uTyPzAkKLFLOZN0psdi8aLkkgudW/bOMrfVOmkGq5QeRi70JZdCwUy+3bLDweOGS/rCwXfifz6KZy3ECsNCisfAu9PjKIoso/tAENFQDIxu5xePJhANReHxeVKvqwYVHKvgrqleNPbJzhKwLDC0sbhdqKo/IoDnOYNWArmmE45lcfQAFi/8LQqR9UAWJdMSD8MwiEVzy5fHYyIO7k8LggWDSXjr0iZtiqIgHpfBsAwmHB3FsQOLOv2CmL1P6piyGx6PG7KsBlH19T5LGYBiyedtUiy5rolk1Mj7mS6dqH9XLMugrs6LREJEMGhlLLx3lz5qDc1YHIYIggsOB2+Q4tZDbIXLwZost5Ly22AhikkL/h7pqQurO5p8mFmtk2CG/B4EwWNoCq3kjpJIkFspuWTuLL93Bo/1G/ZjewcHoV4wvLfxpALOJQNgoCRi6NgdzHl9wa4wZEmCUOdFNBKFk1dw/ffdGDyguEmMXOj7Crq6zINHSZJR75Zx3TkyHv/vbjgFNdtk/hlnIIlylt9JIi5if4dRZZRhGHTsDWPwIC9Ynkc4rJZAjjkihtNbK/c+k4WdYRh0dgZSZUKzDID9Eyg8z6UW9qTlYD2TdPbJ+Hpq35YTXi+vjbvKsgyHgy8raKelj9ojVWgaqlb0+uZNAPB6nXlrklYmOxiGQX29kCX1XQiSpXC7XXA61UZKfVOeOqlR+O0xLwFUHtXUSQDLcloDGwDDmKuxiU29JjuCHp7nUVcnIJmUUg1s9n6Mw1EJsx7cgVgc8Db4wKWuQ0lpiyuyjGSy8HUoigKXQ8FFZ9Xh/DPrCx6fD73XRilZoVBExu9ekcHwDnjr3DmOkuH1ObVzDnbHEQok8+TiFHh9DiQTMk4aruC8kyp3G3E4HKirExCLxQv+fRrHrLMnUErNang8bng82UJblYZhGNTVCWAYFuFwxHBdpYp40dKHOdVu3rziJ9trutYun3MUbd60m1gskTcbYM3vo/SMhX6ENBqNaqlR424lXYMlu399toD0M4hi4RKA3RiFrowBVb5Sg8dTnClZLvJNudiJ18Ph1mv647dP7kbwQHb62eN1AXlEpQC1tPEfEz344fl98vYwFIO+d6VURUefwOLOHwCPvhRHRygBX70LHsFp+MwqCgNZkiGKMjoPxCCK+V9AUYB9e0IY7+dx3kmVu8V4vQKczuKlsc2E1nL1NeTLapDyg6IAXV2BqtbH1aCZOJKSvy2pKM+QZFLExo0b0b//APh8Xlr66EHI4uFVCqEZC6jjpvnWfnVqwIlQqLyRtYYGH7q6MnUUs9E3ZxYD2amQ3QoRumIYBizLIBSKIpms3k4qXXIBQqHyNAP0pmQkq1HI8howLq7hcLQqgdTKj0N45o/7EI0Zr1OBArcgmE5+AECdwODBHw/GkQOdWq28XK0B/Vijld6VzoCMx/+YRCiigOUYeLzOVLOpmonhGBlSUfsQBZCS+P4ZDpw0vDKbPr00trWRymwKZTWIf0655mFWIBmSYhxJ9ZC/KYZh8OMf34a1a9eiX7/+GDmyFa2tYzB69FgcffQxFTzzQ49qZywuuW1rTdfa1+cdR3Us7KZQYEHMxoLBSFk/v08fHwKBUN4boCzLNjRnOiEIHm1BL3ZRtgNy06uEaqdeA8Dh4FPlk/T8v9vtrKhRWi5YlgXDuvDw3G3Y2GaUd2cYwOU1TkgoioKh/RncfWM/NPRxGHRCSFCof6/yfV5IU6oo2lfuiSVkPP5yAvu6zL6rqIJtztzBBccqGHcc8MNz3HC79FbepfnU5IMopVar/JCZ1WDZ4vVP7EItK6YDdit/w2pGRsaXX36JTZs2YuPG9fjqq+2YN2/RYS14VSrVDiwu+tHmmq61byw4ngYWdsOy6n+5v8/C53MjECg3sPAiEDC/+as3CdnSwkD8PdQsRcRwoyOLMlnA7O5pUBc4AbKsWL7pFQspn7hc2cqGxSzKdkCCOLJz3fFNHAue24Ntu5I6vQnA5XGBYVmI8TgG92Mx+56hpqUxvTQ0ea/0tXL9opzLRMsOIjEZC19PYte+7F+goigQfOZCYCwjY+rZCoYNNZaA7BJaI+UHAKmpreqljjMzJAxjntWoRADvcKilj0z/nNKhUx+lUO3A4vs3t9V0rX1zoZ8GFnZTKLAotwGTUF8vIBSKGW6Gdo2Qkh1csalZfU8DSY+S3SS5KRYLEboKhyMlS51bIdPOXRQlw40+u9FVsm0h0pu0mZV7vtoZw+t/PQiOA1xOFh4Xg0EDnZg4rg4+b2n9BmaLMqBmt8LhaEWzM+/8K4n314kQpWwbeI83LQSmKArkZBK3XMJhcP/CYlp6oTXSbFhoUSZ6HLUoP5B+oXyfcaNaKJcK4Av3ahSCiHyVojdjhnqLJwEFnfoohmoHFhfe+FlN19q3F4+kgYXdFAosgOL7JMyoqxMMxmV2+HsYMwXl7+DITjnzRp9PUbMW/QwEssjE4/llmrPLJ9Zv9JlZimpCSk2k8bDY98oKSVHGn/+ZxIebZCQyAgy3xwlJksHKCfzwHCfGHl9+k6Z+Qda/V6Iogud5cJxxsqgaqJMX3rLNw3L1ahST1Ui7sMoIBq2VuejUR3lUO7A4f9qGmq617z47mk6FHGqQyZBSmzPNIJMPaqbA+gipomRbQ6cloY3qk+nMQPWFrtIiRFxRUwBEkpzIe+tv9O6UnHWmqmGuG7jRSr5yOiBmkIZYRVFMJxDyvVeZk0Kl4nY5MO3iBlz7PQl/W9WFr/fK8LoZeD1AnSBi2FAedV7rdXnyPujfK5fLCY9HHX8lGapMqfVKQbRA4vHCI6y5yJxAIT+30ARKuY6k2dDSx6GEQpU3ey8MY+4tUghFUTTTK6D8RUnv71HJEVIzRU2yW1dRUlLKnC2GZIUgUslWFEOzRw0ZLavh8bg1u2ujTohc0ywFScPnW2Tyje+WGkDpISU2EryeMtqBU0bbeXW5cbudhh6SfFLrdgRQeuyasjEjn7Im8aoBgHg8kRIsY8rq1VDfXg5qUEFLH4cCdn1+ewo0sEBxwYJ6M2ZQavlClhXEYnG43S40NdVBlhWD9kQxKVayW1czBdU1VWJZBoLgTmUKghBFVUaYLF5pQzK1lyHdPGk96CHd8CzLoLs7ZOsfn76zn6Cf//d6PWAYddwyFjNXZK0U+gxJV1ewpDR8tgdFOoASBHeq/yQ7gNK/tpqGN8+QVBL9a+sD50JS61YCKP1r19dnm4dVEhLsiqIaYCQSScRica0xWQ2gSivhVbv0ceDAfixevBBbt27B008/DwAIBLqxcOF8tLQMws6dOzBjxi1oamrOeu57772LzZvbwHEsWloG46KLLq3KOfdElCo2I1cDGlgUCSlnFHvD0TdnJhJpARvip6GK13i0LvlcNw6yY7bD36NUcr22ek3JLEMydffvAs8bDcnKGTMkWQrr3fDFQ8oniqLA4eARjcYhSWqdPzOAqlRKPn3d9mRICgVQ+s8ggJS0vf0jw4VIG3gV99r5Aih9BiqfKV72axc2D7MbM0dS/XtlltUgvRrxeAIHDhxAnz4NqFXpY/36TzB58rewZctm7bEnn3wCEyacjLPOOgcrV36AJ574Pe6//xHD8zo69uLll1/AkiUvgmEYTJ9+DU488SQMGTK0aufek5BpxqJ3Uor6pr45M/M5xE9Db0duVvuXJAkOhwOKUll/DzPUnaMAoLieAv2OklBqABbyoFUAACAASURBVKV/7Vr1M5AMSeZrk2mAchxdS31tNTtT2esmART5DJI+Do5jIcuyNu1TDf0TOwy8APMASv0MprM1maqukiRpTr/V/qwRCXae5/O+tplfCLlf7N27B9deew1cLhdGjBiF1tYxGDVqDI4/3g+n09w4zm6+/e2zsXbtx4bHVq/+F665ZhoAYMyYsfjlLx/Met6HH66G3z9cG11ubR2NNWtW9d7AgvZY9E6KkeYuZ4TUrPbv9XrgdrsgyzI4jgghVce4i9TWre5a8wdQTrAslyUI5XIRKfDq9zMUkyEp1tFVP+ZazJggadgrxu/CbvSv3d2dfu10mSFt4KXP1NhRltIbplUiG5c2xUv/baXdQj3gOC7lwJpMjYhaF/AqBo7jUF/v1STYS4V8Bpubj8Bbb72L3bt3Y/36Ddi4cQP++td34HK5sWjRsxU48+Lo7DwIQVA1RwTBi2AwoE34pI/p1I4hx3V2Hqz6ufYU5MPMhIwGFii+xyJfYKFXzizXV4Sk3FWL724tiiUpXrfbaWhcK7fMYIYqAqSOr5Za1y+GfM2TguABz2c2rrFVuclbzRSYObqSRdnrdWbpNOgDQ/2ki909JIXQm5aZTdmQoK9SPQ2VbJLMBZmA4jgOLMsiGFR1SNTAUO+rYSx32QlpyLUubqaWPhiGQUvLULS0DMWUKRfYdp5WaGxsQiQSRl1dXer/9YagQj2mETt3fq19HYmEMWjQkGqfao+BlkJ6KbkCC71yZrkBRVrwyWFqnkVS12QXz3Gs6S65XI0GYi9eTQdUEhzxPAeOYxEOR7VdDbGEzmeyZgeV6OPI7D8BzEdCJUkGz3OIx5MIBkvftVqBWH2XYlpmV08Dx6kNmtVskiTkMg9TP1dx7RhS7iIBrx2y5CSIZFnWcuDe06c+Jk06DRs3bkD//gOwfv2nOPXU0wCom4uOjg4MGDAAJ588Ca++uly7r27cuAGXXvqDGp957fjnm6f3vDfSAlQgKwVfIMTyeFypXbe6YNilnKkXfIpEomWNs+p3yQ4Hb1pmMPu5egfUUMh+e/F86PUZcgl85TJZK8f51Phz01mKYDBS5UyBusA4HDxEUQLHsZYcXUulknLgpCxERKEyy0I8z6VULKsXwBKsqHdalSUngVwikcwr6lYYBYpCmjN7hjbFunX/h7/+9R38+9+rcdFFl+LKK69GPB7HwoV/QP/+A/DNN7swc+ataGpqxpYtbXjkkf/C88//EYA6FfLFF5+DZVkMGTK0R02FVFsg63CDBhYpCgUWbrfaDBWLJWxRzkz7e7C2qwrqd5NG34n0jVAQ3DkzJJWGqEiWusCU63yqpxbTJgR9T4F+gbHjugqhzxRUK4jUB7wul2rFbvwcVq4pVA8J5FRpbOt/Z6XIkqcdSSOw4jScluWmglfVgAYW1qCBRYpCDqculwMsq6bs7fP3qN7iRm6ETqda9yf1ZqvTDKWQ7uOQU1kK6x8vc+fTbJO1WmYpgNJ7CvI5upZaFkr7XdQuU0AaU7PluxUtW2N3uauS9uqZmMmSqyiWVWrT2hQ9s/RxOEIDC2vQwCJFocBCXZgEw9hkqTdCfYOkFX+PctA3Cqo7VjnLjKwc18liqVYfh5nJGmkGjceTCIfLc6gtF30/gxVfFf11FWuzrh+fLcfvwiperwCnM3+mIFe5q9ymUEItgymSmSKZi7RXSKkaKLUtfeze/Q1uv/1m9OvXH4DaYHnsscNw330Pase8++6f8cYbr2njrRde+P0e00RqBRpYWIMGFilyBRaZtuZGcyFj3T+fO2jaCbT6Nzq9JHauccbMPo30jdCaFblqluaFJFW/j4MsrBzHIpkUwXFc3ikNuyHBVCX6GYzlk2xHV4Zhaza6ayVToC/jkSbKUrRCrJqHWUUQ3HC5XFmZKaMDKq9lDXPJkveE0kd3dxc2b27DSSdNBAA888yTmDBhIsaOHacd8+67f8b48Sdi4MCWmpxjpaCBhTVoYJEiM7AotjkzV308Ldaj1MwJ1GjxXVr6X6+mSf5fan2cpP9r0ceRr5ci8/3Sj+/aURYiC2u1gyl1QXakxkGZrOuqhjsoKfPZGUylm0I5LQtlNhJqh3lYuejlyIPBcFHveWYWat68uVi3bh1GjmzFyJGtGDVqNPr0aazC2RcmkUjgvvt+it/+dq7h8Xff/TO+/LIdTU3NiMdjuPTSK1Bf36dGZ2kfNLCwBg0sUugDC6vNmWQu3u12aql4fT9DNRrW0n0c9u1Yi+1nqKWtOilZqToFxQVTRKGRXJeVslC6MTWiTRBVi8zm0FzZNatlBjPIKCeAVKagcu+5PrtGmifVDQCDWEwVdqumkqGViRM9kUgYmzZtwvr167F+/Xp89tkmHHHEEfjRj27H5Mln2HjGpfPOO2+B53l85zvnGx7/5ptd8HgENDY2YvXqlXjllRcxd+7CGp2lfdDAwho0sEjBsoAaSFgfIU2XHtQR0lwLciUaJ1WlTiHvGKd9r5Xdz0Dm0mvpu2BVwTJ3WSi3yZpxfLayC6sZanbIkbdRMFeZIZchWbHYtbCWgz5TQHRRSPNkKeZd5UJ+71YnTsxKH5IkYdu2L9Hc3IzGxiY7Trds7rrrNsye/ViW0JWeeDyOc889A//4xyrNqfVQhQYW1qACWSkURYaiyCnlzPI+U+riQjw20kqKROCKiPDoF2Q7BK4IRKOgWn0cetEksltWH5Pgcrng9QoZfRr27ZD16LMUdihYlmqyxnFsVX/veoxiV8G8v99SDMmKydYY/S6qqxwK5Dcuy5SQ1/cMkVKllc+i0Q01/++9ELmmPjiOw3HHDSv759rF2rUfo7V1jBZUBALd4DgOXq8PixbNx/TpM8HzPHbu/BoDB7Yc8kEFxTo0sEhBuq/VP3IFpAyiZi4KBxokBV6Mx0amiqF+h+x2e0sWgjJKgVdXzTCtGsrnbFgzqjNKGTtka+dqzFJUxv01l8lapr260+nQ6v/V6GewQ+wq05BMXZC5go6uadGn8vwurMAwSDXl5jYPy5aQ1/ufWDOQs88NtecJXpnx5puv44477ta+fuGFpair64OpU69DU1Mz5syZjYEDW9DevhU///nDNTxTSk+BlkLyQm40uQONXbu+ht/vB8sytmkzqCnrdCpe3xCqv7kzDCAIApzO2ghdqQurkCX4lA+9iiFJWSeTyaw+jULoXTFroUtBLOVJIKm3ty5F/bQcqll2yWziVXetpJ8hjlgsXlVXUPtULM17awopoPp8aoZG9Rmxt/RB6TnQUog1aGBREor2XzAYxOLFC7Fy5T/x3HPLKt4JbZxk4FNlG1Yb6auu5bNeE8NabVmvY5B5c881vmtXL0V555vWhgiFwjl/7/nUT0kGoJx+BqLPUIseFtLPABBH0PSURqmOruVAsoKVGN8FzCe8yHsmSTLcbhdEUUQoZE0LhQpe9XxoYGENGliUwfvv/wOPP/5bTJ58BmbO/BF8Pl/qOySrUbnXJos6z3NIJJLawlzuzr9U0kqKamOq3ZCbe6ZcctpaXa2XW90xloNVOXCzbE2xJmvFBjSVIn8/Q/aUhlmGrVz05mHVbozleQ4ejxtOpwOKolhsCq196eOmm67TxKw4jsua4IjH43jiid+jb99++PrrHbj66uswdOiRtTjVmkIDC2vQHosSURQFK1b8HQ899GuDUEzqu1BvHul/A8X3aRRCP20SDBr7CfQ7f4/HDSsjk2awLAOvV81SmNls2wWRGs90B3W7XfB41HFG/e7RLtv4fOjLLlaaFM37GbKtyDNT8empi+r7mxivPVc/Q3GOrmajyYWo9bV7PG5wHIvOzoCm4EqyGW537h6UTIxZitqVPiZOnIQbbpiR8/vLl7+M/v0H4KqrrkV7+1bMnv0IFix4uopnSDkcoBmLipIOLqwEGmnDsuJ9LsxGJvU39lK8C2pZejAruxDBpHJ2/qWS6XVRScxS8eTvMxqNIR5PVHW3nhacsp6dMhtNLtTPUIwkeKUotpcjW1FTLVPu2vUNPvjgAwwfPgJDhhwJluXRE0of9933U4wYMQrxeBwjRozCqadONnz/Rz+ajhkzbsHYseMBAOee+y386U/vwOv1mf24wxaasbAGzVhUlMwbSekZDVJTL1UjIN/IpCCoExqFpK31AU1txgnV5tBYLG7I0EiSBEnKt/Mv3KdRCDLtwvN8RTM0evTZmrTfRBKiKIHn1UxUuTv/UinVNK0QmZNQ+iBKEDwGqXV9RqqrK1BR8zAzSlEP1U8MRVPxB8exiMdjWLduLZ57bikOHuzEqFGjMXr0GEycOAkjRoyqwlWYc9VV12LkyFZIkoRbb70RgiBg3LgTtO93dh6EIAja116vF52dnb0usKBYgwYWVcVsxyLrAg31/wyjYNu2bViy5Fn84he/QCKRtJzuNxuZ1EtA+3yqORpZsFiWhcfjqonokT5LUcyinj1amF601OCgtJq/XsGy2qOUQK5FPVsDhZS8rAZRevT26uqiXplV3azkpQZPLrjdLiiK+j54vV5dEFXZ4E7vM9LVFSg7OyRJMhoajsA999wPgEFnZxc2blyPDRvW4y9/ebumgcXIka0A1P6KMWPGY+3ajw2BRWNjEyKRdHNqOBxGY2PPkBWnHDrQwKLmGOutiUQczz33DN5883XccsssSBLAMBIqkUIlNf/0Titbm0Gtk6MqN3bAWHrI7CMpllx9Gumav1HDgPRpEMEnM02OaqD3GMm1qOfa+auLsHHnX6rJWi0dQRmGgSC4wDDpfgZ9EKXvQanECK+dPiOZUx+NjU04/fQzcfrpZ1o/UQt89dV2bNjwCS688CIAwM6dO/Ctb/2HQfBq0qTJ2LhxPcaOHY/29q047rhhNFtBKRnaY9GDEEUR06ZdhcGDh+LOO+/GEUf0Re4+DftfPz3KaNRmSFtak90x8T2xL9Cwc4S1GPR9GjzPa79PSZIRDkeqXtNPe4xYX9QzNVAKScjX2hG02F6OQo6u5Y7w5nIkLZ3aT33kY//+fZgz5zfw+4cjHA5DFEXMmnUHFi36gyZ4FY/HMH/+XDQ3N2PXrp2YOvV6OhVCKRkaWPQwtm37EkcffUyeI+xpCNVjFFzK7S9iPgpq3Vq9mg2SZpDSQzye0K6xVPXTctF7XVRqlJLjjGZk+okhQA1qavW7FwQPXK7yezmyfXiKHwfVj7EW60iaCyp4dXhBAwtr0MDikMdaoJGWIi9dcEnfEJopAlVMGr7aWYpMeJ5L+Ztk25ubTWiUW2LIRT5tiEpCJoYEwa35OtipO1HcOagBlSzLtlrLF+voaqdxGhW8OvyggYU1aGBxWFJYinzv3j046qihcDictu6UM9Um9Wl4veZEpYW2ClGOz0ZmiUHf7FqKnoZaeiDW7tUXuyIBFVFtVR8zjkya9aDYRTUDqkxHV+IuDADRaDw1wlvutfXs0gelfGhgYQ0aWPQK0lLkiUQCy5YtxZtv/glPPfU0Bg5sqegrp9PwjlQaHlq5JBKJIB6vrr+J2iApQJZlBIPWdspmfRqFXGprXfYpVha7nGsrhNoc6wXP10Y5lTiSyrKCZDKpBVOlOLoS0qUPkqmoLrt27cRTTy2A3z8cHR0d6NOnD66//kbDMe+++2e88cZrmtLmhRd+H1OmXFD1cz0UoYGFNehUSK9ATdF+9tlG/OpXD2PIkCFYsuQFNDc3G0ZdK9EQSqYYgIS2qIqi6mrq8XgM44R2jEvmg+gT2DX1kEtPg0yfZKbhXS4nHI7q6WLoUUsPAhQFRY1Sml8bl7o2IUtwrVB/jV5wqqurMi60+SCaKMYsSWmOroSeUPoIBLpx9tnnapMmV199OSZNmozhw0cYjnvooV9VfPNAoWRCA4texFtv/QnXXXcDzjrrXDCGKKKyUuT5dCnyaU6kFyxriTN9g6QVfYJCmOlp8DwHl8uJ+np1ZE+SJLhcTrBsdXoZgPSiaqWfQL02Wcsw6UsMHo87VT6RtB2/vnxSafOwQvh86ghxLpG37GszWqyHwyHcfPNM+P3DMWLESIwePQ5DhhyV8TdUXTK1MGRZhsfjyTrutdeWo6mpGfF4DJdeekXFzRIpFICWQiim2Dd5Uk4vhXHyJL1gkUCjlMAgc4S22pCpB2Jrn68HxWwU1ApEl8MOm+9iyDRZA9TdvaIoCIcjNdAFYVFX59N6SazEcO3t7di4cQPWrVuHDRvWIxqNYPz4CXjggV/A4XDYd9Jl8P77K7Bu3f/hxz++y/D4N9/sgscjoLGxEatXr8Qrr7yYZTpGMYeWQqxBAwtKEZQeaNg58WHWfFdoMSZy5LXSZtArWOabesg1CmqllwFQd9x1dUJBr4tKQQJKkpVRdVCqM8ILAG63E4LgsaXslS59pBs09+3rwPbtX2LChIk1zVysXfsxPvhgBW677Sdg2dwNpPF4HOeeewb+8Y9V2iQQJTc0sLAGLYVQiqB4KXKAwcqVH0AUkzj//AvLVs/UQxRCzWStBcGdtRirKoKemsiRA6X1cuh7UACjeZzbLYBluZLVJsnESzAYQTJZ/dIDMQ/LV/YifjX68eRSs1FmMAzg83nzurEWT+6pj759+6Fv335WTtUyq1atxKefrsPtt9+FAwf2Y8+e3Rg69EhNRXPRovmYPn0meJ7Hzp1fY+DAFhpUUKoCzVhQbEJBV1cnHnvsUbS3b8WDDz6E448/HtVobiOLsdPpgNPp0PwzEolkxXfGxvNQGyQBIBjMLTRWCvpeBjOtEP1irO8lsSr4VA7llB5yZaPKMVkr1pG0GGo99VGIL774HLNm3QS/X23WjMViuOSSy7F9+5eaiuby5S9j27Z2DBzYgvb2rbj88ivR2jq6xmd+aEAzFtaggQXFFj77bCPuvfcnOPvsKbjpppvhcrlQLSlywDjGGY3GszQnKi0ARbQZqpElMVuMVW8NDtFoHNFo9cdY7fIZyWevnm9qqBRH0kKYlT4ovQsaWFijVwcWsizjrbf+hKefXoR58xbimGOO07730kvPIxwOIxgM4OSTT8Hkyd/Kev7u3d9g6dKnMXjwEOze/Q1uvfUOg+Vwb2Lnzq8RDAbyODfaL0WuPr+4Xg6jiqYqAKUPNMrNLuhfvxbaDERsSx2RlMDznEGy225PF7PX9/nSYl9297IUUkAVRcnGXhoFikIyFDSo6M3QwMIavbrHYuvWzRg1qhVut9vw+KZNG7F27cf43e/mQRRFXH315Rg79gTU1dUZjvvtb3+N6dNnYOTIVrz66it48cXncOONN1fzEnoMgwcPKXBEZp+G9RFX1YlVQDyeKNjLQXa8eidXh4PX3FxVW/lkSSl4vXmWHb0kpaJ//UAg/fr6Pg2jLoO9rqDVuP5c9urpMVdOO8bh4MuerDFmKWqzpnz00b/x/vsr0NjYCIZhMG3aTYbvx+NxPPHE79G3bz98/fUOXH31db3SIIzS8+nVYfnxxw/HsGH+rMdXrfonWlvHAFBvYkceeRQ+/XSt4RhRFLFu3cfaDn306HFYvXpl5U/6sEHfFMdBjXFZKAoHRWFSY4pAOsuheyajahN4vR4Eg+GyJMGJ+FMwGMbBg93o7g4imRTB8zzq631oauqDujovPB4XeD674c3rFeDzCQiFynt9q3i9Hvh8XtPXl2VF6zPo6gri4MEuTeXT43GjqakBDQ11KfM1B1i29IVUEHK/fqURRREMo5ZNAoEQuruDEEURDkdx710m6aCCQ62Cilgsht/97te47bY7ccMNM9DevgUff/yh4Zjly19G//4DMHXq9fjBD67C7NmP1ORcKZRCHPYZizvvvBUHDx7Menz69Bmm5Q0A6Ow8iKOOOlr72uv1obOz03BMV1cXXC6XNmrm9XqzjqGUSmacq6R6IdIllHXrPsbs2b/G44/PxaBBg2175Uxxq8xdP5nOkGUZDgePZFJEV1fAlp1/KZAGSUmSUq9f+ATUbIyxiZX0abhcTvh8QtFNk+kGUbno17cTvSNpZ2f69XNN1qg6HnrRtSS6uwOpkmXPKX1s3LgeAwYM1OS3R48ei9WrV2LChJO1Y1avXokZM24BABx77HHYunULwuEQvF5fTc6ZQsnFYR9YPPbY/JKf09jYhEgkon0dDofQ2NhoOKahoQHxeByKooBhGITD4axjKFZJl0+i0SgWLpyHlSvfx3333Y+WliHaolKJhlCy6ycpeCI25XI5IUkyXC5nVomh0ousXQ2SQP4RXo/HnWqa1JdPpJq5sRIcDh51dd6CDaqZ7x15Lhm7nDr1avTv3x+jRo3GmDHjMHr0OAwaNLimehSdnQcN/Vlerw+bN7cVOEbdzNDAgtLTOOwDi3I49dTTsWTJUwDUtOv27dswduwJAFRX0COO6Aue5zF+/AR8/vkmjBzZig0bPsGkSZNredqHNQ8++DP4fHVYuvQV1NfXpx6trBQ5geNY+HzqGOfBg91aAKHu+h1wu13w+YSy3U4LwbIMfD4vGIZBV1ewImJfRE9DL0dOJjNInwYAxGIJSJIEhmGqmq1QyzZOBALhsvxkyHvSv/9AvPPOe9i+fTs++eQTrFmzCk89tRAulwsvvfRaXpGpSlLMZib7GLqZofRMevVUSCAQwOuvL8crr7yIKVPOx9lnT9HmvF966XkEg0EEgwGccsqpWtlk5sxpuPnm2zB27Djs3v0NlixZjJaWQdi7dy9mzTKfCvnpT29HNJquQ7e3b8Ubb/wlNZKZ5rLLvosBAwYCUAV4HnjgF5W69EOORCKhpYlzY//kSVoSPIpYLH+WINMRFIAh0ChnYqTWbqhpbQgRiUTCVGo9PVlj/+2ClF5kOb+CaXGYlz4URUE0Gq3pRFcsFsO11/4Qy5Yth9PpxH33/RQXX3w5jj/erwleLVu2FCzL4KqrrkV7+1bMmTMbCxY8XbNzPpyhUyHW6NWBRbX4+9//H84661wAqt3xiy8+h7vvvi/ruGeeeRI33DCj2qd3GFN+oKHPEpQ7xkjcTslizLJEkyFZ1BgoMc8KBq1JopdLIfOwTG+QciZr8kGCKjtKLz1d8AoAPvpoDVas+DsaGhrB8zymTbsJCxbM1QSv4vEY5s+fi+bmZuzatRNTp15Pp0IqBA0srEEDiyozd+4cfPe73zdoZhBuu20mJk6chEgkglNOORWjR4+twRke7pDFLluKnNDW9gUmTjwJ8XjSVrEpfXlB3fWbj4GSLEEyad08qxzSQRVSQVVxJ6APpEoRtzKDBFWBgHVtkMNd8EqWZfzsZ3dh06aNmDXrTpx77hT86lcP4auvtuOhh36NAQMG1PoUDzloYGEN2mNhE8VMn4TDIezdu8c0qACAmTNvxciRrYjFYpg27So8+ujvi9CHoJRG7smTQCCAuXPnYPPmNjz77FI4nS6zH1A2mZoMentu4p0hywpYltEUPKsdVJAsQTkKnma28STI8Ho9RSmg6mXBrU/d9Jypj0rCsiwefPBXuOyyCzF+vNoLNnjwEFxxxX/SoIJSE2hgYRPFTJ+8/fabuOCC7+X8/siRrQAAt9uNYcOOx4YNn9LAouKokycff/whfvWrh3DGGWdi8eLn4HC4DaOulRgY0I+Bpn1GGMTjqr16Y2O9wcnVzoZQM4iuRaZ5WLmYiVuRbI3a8Oo1KKAyDGPb1EtPELyqJm63G+eccx7efPN1XH/9jdi+fRuuuWZarU+L0kuhgUWVkGUZ//73GlxxxX8aHuvo6MCAAQPw8ccfQhRFnHLKqQCAnTt3oqXFPp0GSn7eeect3HPP/Tj55FMyvlP5yZN8PiPEVt3hcEAQPGAYGAINOyTEs7UxLP/InJgpoDqdPATBA5ZVJ02IkVy519eTSh/z5s2By+WGIAjYunUzbrvtJ2huPiLrODsaty+++DLMmjUDRx99LCZNOs3yuVMo5UJ7LKrEBx/8L/bt24tLL/2B9tiWLW145JH/wvPP/xHt7Vvx7LNPwu8fgf3796Fv336YOvX6gj/3mWeexLp1/6d9fe2103DSSZmLI/Dee+9i8+Y2cByLlpbBuOiiS+25sF6HfZMnDMNoAk7F+oyQPgZSQmFZNqtPoxTs1MYoB/3USTgcydPwWsz19bzSx1NPLcBNN/0IAPDCC0uxb18H7rjj7qzj7Grc/vGPf4T9+/dhyZKX4HA4LP+83grtsbAGzVhUiTPOODPrsWHD/Hj++T8CUJX0fvnL35b1s+fPfyrv9zs69uLll1/AkiUvgmEYTJ9+DU488SQMGTK0rNfr3WR6ngCAXHJGg+d51NUJSCSS6Ooq3mcjVx8Dz2f3MaQbQs1k0dPmYZXSxigECWr0UyelXF9nZydisTj69OnTY0sfJKgA1NKQx2M+0vrpp+vw4ovPWW7cPv/872H79i9pUEGpKTSwOAx47rln4HA4IcsSLrvsh1mmah9+uBp+/3BNWbC1dTTWrFlFAwvbKCxFTgKNZDKJt99+ExdddBFCIRhktsshXx+D6pXh1fQmSKDBcVxNzdOIIyvDFA5q8l3fihX/wOOPP4Z+/fph1KgxGDNmHMaMGYeWlkFVVdEspnE7GAziww/X4Je/fNT0Z1ht3N61aycGDRqMtrbPccUVV5Z3IRSKTdDA4hAg343r298+GwMHtsDj8eD11/8bjz/+KO69978Mx3V2dkIQvNrXguBFZ2f2z6PYRbaTq6Io2LFjOx5++AH069cXU6ZcCIaxFlTkIrOPQe8LUlfn1Y6RJAkcx1rWmygFNVOjBjWRSHlBDbm+KVPOw1lnfQfbtm3Dp59+gtWr/4VFi+Zj0qTTcM8999t85rkp1LgdCoUwZ85s3Hvvf6G+vo/pMVYbt//7v19BV1cnjjzyKPTvTydBKLWFBhaHAMX6nZx44kl4+eVlWY83NjZi586vta8jkTAGDaLTJtWDwXvv/QV/+MNjuOGGmbjookvAMKhoQ6geUZQgywqcTieSSRGRSFRTCRUEt9YoSTIalRLjIoJbwWDYuuw8MwAADQdJREFUhkwNAKj+JsOGDcewYcNx2WU/hKIoNSnr5KKrqwvz5s3BLbfcjr59++F///fvOPPMs2xv3P7xj++qxOlTKGVBA4tDnCeemItbbrkdAPD11zs0x0/9jevkkyfh1VeXa4ZpGzduMDSR5qKaHe2HO9FoFPPnLza45qap7OSJmXmYKEqmTq5ut9fQEEr+bwW19KFmSrq6Apalv/NNfTAMo/ma9ATuvPMWSJKEhx76OQA1W3jmmWehvX2L1rjd2NiEZ599Eps3f4H9+/fhzDP/A2PHjqvxmVMo5UOnQg5xFi2aj1gshsbGRnz55VbccMNMDB16pGHiBFCnQr744nOwLIshQ4YWNRVS7Y52CsGeyRPiyMrzfNFTJ+rzGINUdzHCVrko1pG0OHre1Afl8IROhViDBhaUoli2bAnC4TBmzrw163tUirwaFJYi15M5xmkV/YirqhAqGwINs/KDIHjgcjlTXif2lD7Mp3IoFHuhgYU1aCmkl9MTOtopxVDc5IksK3j11eUYNKgF3/72WabmYeVgJmzlcPBwOh3wej0GAzJJkiEIHiiKkhLcqlzpg0Kh9DxoYNHL6Qkd7ZRyyJ482bevA4888gAABfff/wDi8WRFpMgBQJIkSJKk9WwQYSuXywmHQ72tJBJJuN3OopxczelZpQ8qRkehFAcNLCg5qVZHO8U6X3zxOe6++w5ccsnlmDr1enAci0pLkeuRZRk8z4PjWHR3B7WvHQ4+JcTFpSZO0iqh+VDPm0NPK31QMToKpTA0sKDkpFId7R999G+8//4KNDY2gmEYTJt2k+H78XgcTzzxe/Tt2w9ff70DV199HYYOPbJi13k4UFdXj0cf/T2GDx+he9SY0ahUoKF6jXghSbLBa6SQk6soSlqgEQyG4HK5UudIMhS1z1JkQsXoKJTC0OZNSlWJxWK49tofYtmy5XA6nbjvvp/i4osvx4QJJ2vHLFu2FCzL4KqrrkV7+1bMmTMbCxY8XcOzPlwprSHUDDLKWo7XiCrc5UA0GsEFF5yPhoYGjB5NFDRPqLqCJpC/56ilZbBBjK6t7fMsMbply5bg4MGDuP32nwBQJ6sAo7Q3pedDmzetQTMWlKqyceN6DBgwEE6nEwAwevRYrF690hBYrF69EjNm3AJA9VDZunULwuEQvF5fTc758KV4KfJM9KOs3d3BstQ71YyFBIDFm2++g6+++grr1q3D6tWrsWjRArAsi4ULn9E0UqoBFaOjUKzT83KNlMOazs6DEIS0EZPX60NnZ2eBY7xZx1AqASlBcNp/isJBUZjUf2rvw9atW3HLLTcjEAigqytgURJcLc9wnAPHHHM8Lr30B3j44V/jjTf+gqeeWop+/frbcmV28MQTc7V/Z4rR7dmzBwBw8smT0Nb2hTYJs3HjBq3/iELpLdCMBaWqNDY2IRJJ6yqEwyE0NjYWOCacdQylGhgbJxVFxmuv/RFLlz6Du+66GwzDQ1HK79MwalMY9zgMw6Bv334Wzt1+OI7D73//O02M7s47/z8AMPQc9evXH1deeTXmzXsMLMviwgu/T/srKL0OGlhQqkpr6xjs2bMbiUQCTqcTGzZ8iosvvhyBQDc4joPX68OkSZOxceN6jB07Hu3tW3HcccNoGaQH8Oijv8bmzV9g0aIlqXHi8htCD0XBKzNxOAAYNsyvKdwCwHe+cz6+853zq3VaFEqPgzZvUqrORx+twYoVf0dDQyN4nse0aTdhwYK5qKvrg6lTr0M8HsP8+XPR3NyMXbt2YurU64ueCtm1ayeeemoB/P7h6OjoQJ8+fXD99Tcajnn33T/jjTde0/o8Lrzw+5gy5QLbr/NwY8uWNhx55NHa7y2bYqTIe/bUB4UC0OZNq9DAgnJY8fnnm7B//z6cfvqZAICrr74cP//5w4YxzHff/TPGjz8RAwe21OgsexOZkydATxG8olByQQMLa9BSCOWwYsSIUYavZVmGx+PJOu6115ajqakZ8XgMl156RU5VUYpVemYA8dOf3o4o0ScH0N6+FW+88ZeUlkYa6txLoZQODSwoVWHx4oV44YWlmDHjFowdewIeeeR+nHfehbj22hsq9prvv78CJ588CUceeZTh8XHjTsCkSZPR2NiI1atX4v7778HcuQsrdh6UnseUKRfgrLPOBaCWz1588bmsoAIAzjvvQurcS6GUCC2FUKrGwoV/wN69e/C9712MrVu34IorrqzYa61d+zE++GAFbrvtJ2DZ3LvmeDyOc889A//4xypwHFex86H0XObOnYPvfvf7OOaY47K+R517eye0FGINmrGgVI3p02di+vSpeOGF5zBnzryKvc6qVSvx6afrcPvtd+HAgf3Ys2c3hg49Ups6WbRoPqZPnwme57Fz59cYOLCFBhWHIcU494bDIezdu8c0qACocy+FUg40sKBUDYfDgREjRmHNmlXo7DyIpqZm21/jiy8+xwMP3Au/fwRmzZqBWCyGSy65HB98sEKbOmlqasacObMxcGAL2tu34uc/f7ik17jppuu0yQiO47LKKNTrpGdQjIrm22+/iQsu+F7O71PnXgqldGhgQakaf/3rOzjttNMxaNBg/OY3v8BvfvO47a8xfPgI/O1v/8x7jNUSzMSJk/LW3Zcvfxn9+w/QvE5mz36Eep30QGRZxr//vQZXXPGfhseocy+FYo2e2bJNOexYvvxlLFmyGPX1DWhpGYw1a1bhgQd+ZujMP1T48suteOGFpXjmmSexatXKrO+vXr0Sra1jABi9Tig9i5UrP8Bpp002GJ21t2/B3XffDkBVgP3zn/+E559/Fo899puinHspFApt3qRQSuazzzZi5MhWSJKEW2+9ETNm3Ipx407Qvn/llZfg4Yd/jWHD/ACAiy8+H3/4w5M0hU6hHCLQ5k1r0IwFhVIipO7OcRzGjBmPtWs/Nnyfep1QKJTeDA0sKJQS+Oqr7Xj77Te0r3fu3IHBg4cgEOjWyh3E6wQA9TqhUCi9DloKoVBKYP/+fZgz5zfw+4cjHA5DFEXMmnUHFi36gy1eJ7t3f4Pbb79ZswuPRMI49thhuO++B7VjqNeJ2mT51lt/wtNPL8K8eQsN46IvvfQ8wuEwgsEATj75FG20VM/u3d9g6dKnMXjwEOze/Q1uvfUOCIJQzUug9GBoKcQaNLCgUHoQ3d1d2Ly5DSedNBEA8MwzT2LChImGpkHqdQJs3vwFGIbBvffehUcffVwLLDZt2oglS57C7343D6Io4uqrL8fixc+jrq7O8Pw775yF6dNnYOTIVrz66ivo7OzEjTfeXItLofRAaGBhDVoKoVB6EH36NGhBRSKRwBdffGY6ifDaa8vx0kvLsGTJYgQC3dU+zZpz/PHDteZYPatW/VObyOF5HkceeRQ+/XSt4RhRFLFu3cear8zo0eOwenX2dA+FQikPqmNBofRQ/va3v+Lss7+T9Xhv8TopRjkzk87OgzjqqKO1r71eHzo7Ow3HdHV1weVyaWOmXq836xgKhVI+NLCgUHooK1b8D2bPfizr8ZaWQdq/TzjhJNxzz08gSdJhJ0tejHJmJtkTOaGsiZyGhgbE43EoigKGYejUDoViM7QUQqH0QNau/RitrWPA82rsr586WbRoPkRRBADqdZLBqaeerk3kiKKI7du3YexYVWNk7949kCQJPM9j/PgJ+PzzTQCADRs+waRJk2t2zhTK4QZt3qRQeiAPPPAz3HHH3WhoaAAALFgwV5s6Wb78ZWzb1q55nVx++ZVobR2d9+cdOLAfixcvxNatW/D0088DUIOVhQvno6VlEHbu3IEZM24x9W957713sXlzGziORUvLYFx00aX2X3CJBAIBvP76crzyyouYMuV8nH32FO138NJLzyMYDCIYDOCUU07VyiYzZ07DzTffhrFjx2H37m+wZMlitLQMwt69ezFrFp0KoaShzZvWoIEFhdILWLHif+BwOLFkyWI888wyAMBvf/srnHDCSTjrrHOwcuUHWLHib7j//kcMz+vo2Iu7774DS5a8CIZhMH36NXjggV9gyJChtbgMCqUq0MDCGrQUQqH0Ar797bOzduSrV/9L2+WPGTMWq1b9K+t5H364Gn7/cK3RsbV1NNasWVX5E6ZQKIcsNLCgUHopnZ0HIQheAIAgeBEMBrTejfQxndox5LjOzuxJDQqFQiHkLYVQKJTDB7/ffyaA37W1tU1Iff01gFPb2tq+9vv9TQC2trW1NWU854bUMTekvp6XOm5edc+eQqEcKtCMBYXSe3kHwKTUv09LfQ2/38/6/X7SRPEegBP9fj+pOU8C8JeqniWFQjmkoBkLCqUX4Pf7vwXgGgBTACwEMAeAB8BvAHwF4FgA97S1te31+/3jACxra2sbnXru1QAmAJAAbG5ra3uyBpdAoVAOEWhgQaFQKBQKxTZoKYRCoVAoFIpt0MCCQqFQKBSKbdDAgkKhUCgUim38/4py/va06Oq4AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 720x432 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(10, 6))\n",
    "ax = fig.gca(projection='3d')\n",
    "surf = ax.plot_surface(X, Y, Z, rstride=2, cstride=2,\n",
    "                       cmap='coolwarm', linewidth=0.5,\n",
    "                       antialiased=True)\n",
    "ax.set_xlabel('x')\n",
    "ax.set_ylabel('y')\n",
    "ax.set_zlabel('f(x, y)')\n",
    "fig.colorbar(surf, shrink=0.5, aspect=5)\n",
    "# plt.savefig('../../images/ch11/math_14.png');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Global Optimization"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {
    "uuid": "72b2e44d-2127-412e-9046-2b0c7c5bf7c6"
   },
   "outputs": [],
   "source": [
    "import scipy.optimize as sco  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {
    "uuid": "e6c829bb-f358-430d-9e8c-781e9d15c9e6"
   },
   "outputs": [],
   "source": [
    "def fo(p):\n",
    "    x, y = p\n",
    "    z = np.sin(x) + 0.05 * x ** 2 + np.sin(y) + 0.05 * y ** 2\n",
    "    if output == True:\n",
    "        print('%8.4f | %8.4f | %8.4f' % (x, y, z))  \n",
    "    return z"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {
    "uuid": "d1f54d32-6cb5-4cd2-8a95-ea3b92c87266"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-10.0000 | -10.0000 |  11.0880\n",
      "-10.0000 |  -5.0000 |   7.7529\n",
      "-10.0000 |   0.0000 |   5.5440\n",
      "-10.0000 |   5.0000 |   5.8351\n",
      "-10.0000 |  10.0000 |  10.0000\n",
      " -5.0000 | -10.0000 |   7.7529\n",
      " -5.0000 |  -5.0000 |   4.4178\n",
      " -5.0000 |   0.0000 |   2.2089\n",
      " -5.0000 |   5.0000 |   2.5000\n",
      " -5.0000 |  10.0000 |   6.6649\n",
      "  0.0000 | -10.0000 |   5.5440\n",
      "  0.0000 |  -5.0000 |   2.2089\n",
      "  0.0000 |   0.0000 |   0.0000\n",
      "  0.0000 |   5.0000 |   0.2911\n",
      "  0.0000 |  10.0000 |   4.4560\n",
      "  5.0000 | -10.0000 |   5.8351\n",
      "  5.0000 |  -5.0000 |   2.5000\n",
      "  5.0000 |   0.0000 |   0.2911\n",
      "  5.0000 |   5.0000 |   0.5822\n",
      "  5.0000 |  10.0000 |   4.7471\n",
      " 10.0000 | -10.0000 |  10.0000\n",
      " 10.0000 |  -5.0000 |   6.6649\n",
      " 10.0000 |   0.0000 |   4.4560\n",
      " 10.0000 |   5.0000 |   4.7471\n",
      " 10.0000 |  10.0000 |   8.9120\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([0., 0.])"
      ]
     },
     "execution_count": 63,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "output = True\n",
    "sco.brute(fo, ((-10, 10.1, 5), (-10, 10.1, 5)), finish=None)  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [],
   "source": [
    "output = False\n",
    "opt1 = sco.brute(fo, ((-10, 10.1, 0.1), (-10, 10.1, 0.1)), finish=None)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {
    "uuid": "dc42167b-4e8f-462c-8aad-a94afdf0a8bc"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-1.4, -1.4])"
      ]
     },
     "execution_count": 65,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "opt1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {
    "uuid": "ec2669cd-36a5-4b79-a90c-761a39b12044"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-1.7748994599769203"
      ]
     },
     "execution_count": 66,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fm(opt1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Local Optimization"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " -1.4000 |  -1.4000 |  -1.7749\n",
      " -1.4700 |  -1.4000 |  -1.7743\n",
      " -1.4000 |  -1.4700 |  -1.7743\n",
      " -1.3300 |  -1.4700 |  -1.7696\n",
      " -1.4350 |  -1.4175 |  -1.7756\n",
      " -1.4350 |  -1.3475 |  -1.7722\n",
      " -1.4088 |  -1.4394 |  -1.7755\n",
      " -1.4438 |  -1.4569 |  -1.7751\n",
      " -1.4328 |  -1.4427 |  -1.7756\n",
      " -1.4591 |  -1.4208 |  -1.7752\n",
      " -1.4213 |  -1.4347 |  -1.7757\n",
      " -1.4235 |  -1.4096 |  -1.7755\n",
      " -1.4305 |  -1.4344 |  -1.7757\n",
      " -1.4168 |  -1.4516 |  -1.7753\n",
      " -1.4305 |  -1.4260 |  -1.7757\n",
      " -1.4396 |  -1.4257 |  -1.7756\n",
      " -1.4259 |  -1.4325 |  -1.7757\n",
      " -1.4259 |  -1.4241 |  -1.7757\n",
      " -1.4304 |  -1.4177 |  -1.7757\n",
      " -1.4270 |  -1.4288 |  -1.7757\n",
      "Warning: Maximum number of function evaluations has been exceeded.\n"
     ]
    }
   ],
   "source": [
    "output = True\n",
    "opt2 = sco.fmin(fo, opt1, xtol=0.001, ftol=0.001,\n",
    "                maxiter=15, maxfun=20)  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {
    "uuid": "e451a278-e2ae-4d86-b357-f230468052a4"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-1.42702972, -1.42876755])"
      ]
     },
     "execution_count": 68,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "opt2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {
    "scrolled": true,
    "uuid": "0352d556-6ea7-47a6-9c76-e4a56c0efed7"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-1.7757246992239009"
      ]
     },
     "execution_count": 69,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fm(opt2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {
    "uuid": "ff9beaf9-73d7-4157-85cb-24783abae775"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Optimization terminated successfully.\n",
      "         Current function value: 0.015826\n",
      "         Iterations: 46\n",
      "         Function evaluations: 86\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([4.2710728 , 4.27106945])"
      ]
     },
     "execution_count": 70,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "output = False\n",
    "sco.fmin(fo, (2.0, 2.0), maxiter=250)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Constrained Optimization"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {
    "uuid": "703a8ac0-1c74-4851-9fd3-7ac404ee3446"
   },
   "outputs": [],
   "source": [
    "import math"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {
    "uuid": "703a8ac0-1c74-4851-9fd3-7ac404ee3446"
   },
   "outputs": [],
   "source": [
    "def Eu(p):  \n",
    "    s, b = p\n",
    "    return -(0.5 * math.sqrt(s * 15 + b * 5) +\n",
    "             0.5 * math.sqrt(s * 5 + b * 12))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {
    "uuid": "703a8ac0-1c74-4851-9fd3-7ac404ee3446"
   },
   "outputs": [],
   "source": [
    "cons = ({'type': 'ineq',\n",
    "         'fun': lambda p: 100 - p[0] * 10 - p[1] * 10})  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {
    "uuid": "703a8ac0-1c74-4851-9fd3-7ac404ee3446"
   },
   "outputs": [],
   "source": [
    "bnds = ((0, 1000), (0, 1000))  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {
    "uuid": "8f989832-637a-4188-b096-26ceeabd77ea"
   },
   "outputs": [],
   "source": [
    "result = sco.minimize(Eu, [5, 5], method='SLSQP',\n",
    "                       bounds=bnds, constraints=cons)  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {
    "uuid": "67c11995-124c-4f9d-8edf-1364b412e754"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "     fun: -9.700883611487832\n",
       "     jac: array([-0.48508096, -0.48489535])\n",
       " message: 'Optimization terminated successfully.'\n",
       "    nfev: 21\n",
       "     nit: 5\n",
       "    njev: 5\n",
       "  status: 0\n",
       " success: True\n",
       "       x: array([8.02547122, 1.97452878])"
      ]
     },
     "execution_count": 76,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "result"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {
    "uuid": "53899a89-8532-4f22-a17f-54d106412867"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([8.02547122, 1.97452878])"
      ]
     },
     "execution_count": 77,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "result['x']  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {
    "uuid": "b8548809-fe3a-4fa4-9496-8d3b6a177973"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "9.700883611487832"
      ]
     },
     "execution_count": 78,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "-result['fun']  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {
    "uuid": "7453e87b-a70d-47b9-8a12-c5c0f01e4b86"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "99.99999999999999"
      ]
     },
     "execution_count": 79,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.dot(result['x'], [10, 10])  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Integration"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {
    "uuid": "6a38567d-4a2d-464f-8de3-7687e1d2916d"
   },
   "outputs": [],
   "source": [
    "import scipy.integrate as sci"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {
    "uuid": "0954e5b6-9874-4bad-a2fb-28273a015e4a"
   },
   "outputs": [],
   "source": [
    "def f(x):\n",
    "    return np.sin(x) + 0.5 * x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {
    "uuid": "afb6151f-5743-4950-980e-18047e066ebc"
   },
   "outputs": [],
   "source": [
    "x = np.linspace(0, 10)\n",
    "y = f(x)\n",
    "a = 0.5  \n",
    "b = 9.5  \n",
    "Ix = np.linspace(a, b)  \n",
    "Iy = f(Ix)  #  <4>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {
    "uuid": "ad78923f-e4c1-4381-9a24-33b4f1ea3c56"
   },
   "outputs": [],
   "source": [
    "from matplotlib.patches import Polygon"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {
    "uuid": "ad78923f-e4c1-4381-9a24-33b4f1ea3c56"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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EIl4wCEOHxrB1q5PatbMYPHi11ZHEYuXLw/DhhSxdepDx4/OpVi20K8HQobFcfXU8X38d3lN6VdBERCTivfaai1mzXMTFeXniiaV4PBF0LkuKVXw8DBrk5eefD/Lqq3nUr+8nLc3OP//ptjraaTmtDiAiInIhfvrJwbPPhq47e+SRX6la9ZDFiSQcud1wxx0+evTwsXixg4svDu8Sr4ImIiIRa88eGwMHeo7usdmixR6rI0mYs9uhZcvwX3ZFpzhFRCQi+XwwaFAM6ekOmjTZR58+ptWRRIqMCpqIiESkZ5/18NNPTsqXz+exx5bjcETgYlcip6CCJiIiEefLL5289pobuz3AyJHLKF++wOpIIkVKBU1ERCLK5s02hg4NTQro3389jRsfsDiRSNFTQRMRkYiRnw8DBsSSk2OnZctd/OlPm62OJFIsVNBERCRiTJrkZs0aB1Wr5vLwwyuw2axOJFI8VNBERCQiLFliP3zdWZBhw34lLs5ndSSRYqOCJiIiYS8vDx54wEMgYKNr1000bJhpdSSRYqWCJiIiYW/CBA+bNzupUSOHXr02WB1HpNipoImISFhbtMjBW2+5sNsDPPLIr7jd4b1Fj0hRUEETEZGwdfAgDB3qIRi00b37RurXz7I6kkiJUEETEZGwNX68h23bHFx8cRa3355idRyREqOCJiIiYenHHx28844bhyPAI4+swOXSVk5SeqigiYhI2MnNhYceCu0WcPvtKdSpk21xIpGSpYImIiJhZ+xYD9u3O6hbN5Pu3TdaHUekxKmgiYhIWPnmGwdTprhxOkOnNp1OndqU0kcFTUREwkZ2Njz8cOjUZq9eJrVq5VicSMQaKmgiIhI2Ro+OYdcuBw0aZNCtmzZCl9JLBU1ERMLCV185+OgjFy6Xn4cfXoHDoVObUnqpoImIiOUyM+GRR0KnNvv0MalRI9fiRCLWUkETERHLjRvnYe9eB40aHeDWW3VqU0QFTURELPXzz3b+7/9CszaHDl2Bw2F1IhHrqaCJiIhlfD4YMSIGgG7dNlGjxkGLE4mEBxU0ERGxzOTJLtaudZCcfJDu3bXXpsgRKmgiImKJnTttPP+8G4B7711DTEzA4kQi4UMFTURELPH00x4OHrTTosVurrpqr9VxRMKKCpqIiJS4+fMdfP65C4/Hxz33rLY6jkjYUUETEZESlZcHI0ce2c5pA8nJ+RYnEgk/KmgiIlKi/v53N9u2OahZM5tbb91idRyRsKSCJiIiJWbzZhuvvBKaGHDffatxOrWdk8jJqKCJiEiJCAbh8cdj8HpttG27ncaND1gdSSRsqaCJiEiJ+PxzJ99+6yQhoZC77lpndRyRsKaCJiIixS4nB558MnRqs1+/9ZQtW2hxIpHwpoImIiLFbuLE0GboDRpk0L59qtVxRMKeCpqIiBSrVavsvP22C7s9yH33rcKuI4/IGemviYiIFJtAAEaM8BAI2OjceQt162ZbHUkkIqigiYhIsfnwQxdLlzopXz6f3r03WB1HJGKooImISLHIzITx40MTA+65Zw1xcT6LE4lEDhU0EREpFi++6CEjw06TJvu49tpdVscRiSgqaCIiUuRSUuy8805oYsA996zBZrM6kUhkUUETEZEiN2aMG5/Pxo03plK7do7VcUQijgqaiIgUqfnzHXz9tYu4OC933mlaHUckIqmgiYhIkfF64amnPADcfnsK5cppxwCR86GCJiIiRea991xs3OigatVcbrlli9VxRCKWCpqIiBSJAwdg4sTQshoDBqzD5QpanEgkcqmgiYhIkZg40UNWlp1mzdK56qo9VscRiWgqaCIicsHWr7fz/vtHltVYq2U1RC6QCpqIiFyQYBBGj/bg99vo2HEbtWppWQ2RC6WCJiIiF2TuXAfffeckPr6QXr20rIZIUVBBExGR81ZYCE8/HVpWo1evFMqW9VqcSCQ6qKCJiMh5mzzZxZYtDqpXz6FTp61WxxGJGipoIiJyXtLTbbzwwpFlNdbidGpZDZGiooImIiLn5bnn3OTm2rn88r1ccUW61XFEoooKmoiInLPVq+18+KELhyPAgAFrrI4jEnVU0ERE5JwEg6H9NgMBGzffvJUaNQ5aHUkk6qigiYjIOZk928nChU4SEgq5444Uq+OIRCUVNBEROWteL4wbF5oY0KvXBhITtayGSHFQQRMRkbM2ZYqLTZscVKuWS8eO26yOIxK1VNBEROSsZGfDpEmh0bP+/dfjcmlZDZHiooImIiJn5dVX3Rw4YOeSS/bTosVuq+OIRDUVNBEROaO0NBtvvHFkUdp12GwWBxKJcipoIiJyRhMmeCgstHHddTto0CDT6jgiUU8FTURETmvFCjuffurC6fTTt+96q+OIlAoqaCIickrBIIwZ4wHg1lu3UrlynsWJREoHFTQRETmluXMdRxel7d5di9KKlBQVNBEROSmvF8aODY2e9ey5gYQEn8WJREoPFTQRETmp//u/0KK0VavmctNNWpRWpCSpoImIyAlycmDiRC1KK2IVFTQRETnB3//uZv9+O40aHaBlSy1KK1LSVNBEROQ4O3bY+Oc/XQAMGLBWi9KKWEAFTUREjvPXv3ooKLDzxz/uwDC0KK2IFVTQRETkqJUr7Uyb5tSitCIWU0ETERHgt0Vpg0EbnTtvpUoVLUorYhUVNBERAeDrrx0sWBBalPb22zdaHUekVFNBExERfL7fFqW9/fYUEhK8FicSKd1U0EREhKlTXaSkOKhS5SA337zV6jgipZ4KmohIKZebC88/H1qUtm9fLUorEg5U0ERESrnXXnOTnm6nQYMMrr12l9VxRAQVNBGRUm33bhuvv65FaUXCjQqaiEgpNnGim7w8Oy1b7uKSSzKsjiMih6mgiYiUUuvX25k61YXDEaBfPy1KKxJOVNBEREqpcePcBAI2OnZM5aKLDlodR0SOoYImIlIKff+9g6+/dhEb66Vnzw1WxxGR31FBExEpZQIB+MtfQovSdu++kbJlCy1OJCK/p4ImIlLKfPqpk1WrHFSsmMett26xOo6InIQKmohIKZKXBxMmhBal7dPHxOMJWJxIRE5GBU1EpBR5+203O3c6qF07i9at06yOIyKnoIImIlJK7Ntn4+WXQ4vS3n33OhwOiwOJyCmpoImIlBIvveQmN9fOZZftpXnzfVbHEZHTUEETESkFNm+28d57Luz2IHfdtc7qOCJyBipoIiKlwPjxHnw+G23bbufii3OsjiMiZ6CCJiIS5RYvdvDFFy7cbh+9e2tRWpFIoIImIhLFgkEYOza0rEbXrpupWDHf4kQicjZU0EREothnnzlZutRJuXL5dOu2yeo4InKWVNBERKJUfn5oQ3SAO+80iYvzW5xIRM6WCpqISJR66y03aWkOatXKpl277VbHEZFzoIImIhKF9u79bVHagQPXalFakQijgiYiEoWefz60KO2VV+7WorQiEUgFTUQkyqxda+fDD13Y7QEtSisSoVTQRESiSDAIY8Z4CARsdOq0jRo1DlodSUTOgwqaiEgUmTfPwXffOYmPL6RnTy1KKxKpVNBERKKE1xsaPQO4444UypTxWpxIRM6XCpqISJT44AMXKSkOqlTJ5eabt1kdR0QugAqaiEgUyMoKzdwEuPvu9bhcAYsTiciFUEETEYkCf/ubh4wMO40b76dFi91WxxGRC6SCJiIS4bZssfH22y5stiADB67FZrM6kYhcKBU0EZEI98wzHrxeG23apFGvXpbVcUSkCKigiYhEsEWLHHzxhQu320ffvqbVcUSkiKigiYhEqEAARo8OTQy47bbNVKyYb3EiESkqKmgiIhHq00+drFjhpEKFPLp122R1HBEpQipoIiIR6NAhGD8+NHrWt69JTIzf4kQiUpRU0EREItCrr7rZvdtB3bqZtGmTZnUcESliKmgiIhFm82Ybf/97aPRs0KA12PWTXCTq6K+1iEiEGT06tKzGDTds55JLMqyOIyLFQAVNRCSCzJ3r4KuvXMTGeunff73VcUSkmKigiYhEiPx8eOopDwC9em2gfPkCixOJSHFRQRMRiRBvvOFm61YHNWpk07nzVqvjiEgxUkETEYkAaWk2XnrJBcC9967B6QxanEhEipMKmohIBBg71kN+vp1rrtlJs2b7rY4jIsVMBU1EJMx9/72Dzz934fH4uPvutVbHEZESoIImIhLGvF544onQxIAePTaSnKz9NkVKAxU0EZEwNnmyi5QUB1Wr5tK162ar44hICVFBExEJU3v22Jg06ciOAWtxuQIWJxKRkqKCJiISpsaN85Cba+eqq3ZzxRV7rY4jIiVIBU1EJAwtWuRg2jQXLpefgQM1MUCktFFBExEJM34/jBoVOrXZrdsmqlY9ZHEiESlpKmgiImFmyhQXq1c7SUo6xJ//vNHqOCJiARU0EZEwsn+/jQkTQjsGDBiwlpgYTQwQKY1U0EREwsi4cR6yshw0b55Oq1a7rY4jIhZRQRMRCRPffefgo49cOJ1+Bg1ajc1mdSIRsYoKmohIGDh0CIYPD+0YcMcdKdSocdDiRCJiJRU0EZEw8PzzHrZtc1CrVjbdum2yOo6IWEwFTUTEYsuX23nzTRd2e5AHH1yByxW0OpKIWEwFTUTEQl4vPPJIDIGAjVtv3UyDBllWRxKRMKCCJiJioX/8w83atQ4qVz5I794brI4jImFCBU1ExCIpKXZefDG0Y8ADD6wiJsZvcSIRCRcqaCIiFggEYNgwD4WFNtq2TaV5831WRxKRMKKCJiJigfffd7F4sZNy5fIZOHCd1XFEJMyooImIlLCdO20880zo1ObgwWtISPBanEhEwo0KmohICQoG4bHHPOTm2mnRYhetWu2yOpKIhCEVNBGREvTf/zr56isXcXFeBg9eo+2cROSkVNBERErIgQMwalTo1OZdd62jYsV8ixOJSLhSQRMRKSFPPx3D/v0OLr10H+3bp1odR0TCmAqaiEgJmD/fwSefuHC7/Qwdugq7fvqKyGnoR4SISDHLyoJhw0KnNnv23EC1agctTiQi4U4FTUSkGAWD8OijMezc6aR+/Qy6dt1sdSQRiQAqaCIixWjqVBeff+4iJsbLY48tx+EIWh1JRCKACpqISDFJSbEzapQHgPvuW03VqocsTiQikUIFTUSkGBQUwL33xpCXZ6N16zTatNlhdSQRiSAqaCIixWD8eA+rVzuoXDmXIUNWWx1HRCKMCpqISBH7+msHb77pxuEIMGLEr8TF+ayOFLG+/PJLXn/9datjiJQ4FTQRkSK0Z4+NoUNjALjzTpMGDTItThTZdu7cyUUXXWR1DJES57Q6gMjZyM2FDRvsZGbaiI+HhIQg8fFBEhJCv/d40J6GYrlAAB54IIb9++00a5ZOt26brI4U8Xbs2EHz5s2tjiFS4lTQJKzk54dmvq1fH/q1di2YpoO0tNN/VB2OIPHxAeLjITERypaF5s39tGgR+pWUpKUNpPi9/rqL775zUqZMAcOG/ardAi5Qbm4u2dnZ2Gw2/vnPf5KamkqlSpXo3r07NWvWtDqeSLFSQRNLpaXZmDbNxcqVoUK2ZYudQODEoTCn089FF+VSrlwBBQVO8vOdHDrkJC/PSX6+A6/XQXa2g+xs2LUr9JxffnHw9tuh39ep4+WaawK0bBmgRQs/1aursEnR+vVXOxMmhJbUeOihFVSoUGBxosi3Y0do5ut3331Hly5dSExM5PPPP2fKlCk88cQTOBwOixOKFB8VNClxfj98842Dd991MW+e87hCZrcHqF49l1q1cqhZ88h/s6lW7dBpF/j0+Wzk5TnJy3OQl+ckIyOGdevKs3p1RdavL8fmzS42b4YPPgg9vnp1Py1bBmjZ0k+7dj6qVFFhk/OXmwuDBsXg89m45ZYtXHXVXqsjRYUdO3bgcDjo378/FSpUAKBz585MmjSJ/fv3k5ycbHFCkeKjgiYlZu9eGx995OK99+zs2OECQiNjf/zjbq64Yi+1amVz0UUHcbsD5/zaTmeQxEQviYleAGrVyqV5831ACl6vjU2byrJmTUVWr67A2rUVSEtzMW2ag2nTXDgcQW680Uffvl7atPGjf5TLuXr88Ri2bnVQu3YW/fuvszpORAgGgwSDQeynOQ+8Y8cOmmzJVtEAACAASURBVDRpcrScAbjdoT1NA4Fz/zkhEklU0KRYBYOwcKGD99938cUXTny+0GhZ5coHuemmVNq1207ZsoXFmsHlCtKwYSYNG2Zy222b8Pth27YyrF5dgRUrKrF0aTKzZ7uYPdtF1ao++vTx06uXl2rVNKomZ/af/zj55BMXbrePxx5bfl7/wChNvF4vc+fO5aeffsLv99OqVStuvvnmkxa1nTt3cuWVVx532/bt2/F4PFSqVKmkIotYQgVNikVubmgPwvffd5GSEhqSstuDXH31bm66aRt/+EO6ZRdQOxxQp042depkc+utW8nI8PD119WZO7cmu3bFM3GikxdecNOunY9+/bzccING1eTkNm60MXx46LqzQYPWUqNGrsWJwt+0adNYunTp0a+//fZbYmNjadeu3XGPKywsZN++fQSDv/1DKRgM8v3333PZZZfhdOrwJdFNn3Apct9+62DYMA9paaFWU758Hh06bKd9+1SSkvItTnei8uUL6N59E7fdtomVKysxe3ZNFi2qwty5LubOdVGtWoDevb307q1RNfnNgQPQq1csBw/aueaanbRvn2p1pLCXk5PDsmXLAPjTn/5EmTJlmDJlCgsXLjyhoO06PNtnyZIl1KtXj/j4eObMmUNmZiZ33XVXiWcXKWkqaFJksrLg6ac9fPRR6BqR2rWzuP32FK6+eg9OZ/gXG7sdmjffR/Pm+8jIcDN/fg1mz67Jzp3xTJrk4W9/c9O7t5dHHilUUSvlCgqgf/9Ytm51UKdOFg8/vELr8J2FnTt3Hh0Ru/zyy4mJiaFRo0bEx8dTWFh49PoyCF1/VrFiRW666SamTJnCwYMHadiwIQ899BAJCQlWfQsiJcZ27PBxuEtPz4mcsGeQlJRIenqO1TGKzOzZDh57zM2ePU6cTj+9em2ga9fNEVHMTicQgFWrKjJrVi0WLqxKMGjD7Q7Qv7+PoUMLqVw5sr8/OXfBIAwdGsMnn7ioUCGPl15aQMWK4TcyHI6WLVvGhx9+iNPp5Pnnn7c6joSphIQEGje+3OoYRSIpKfG8/+mmETS5IPv22XjySQ8zZoRmZTZseIAHH1wZNdfi2O3QrNl+mjXbz/btCUyd2oAff6zGW2+5+eADJwMGeHnggUKOmWQmUe6VV9x88okLj8fH6NG/qJydg4KC0NpwMTExFicRCX9a51rOSzAI//2vk2uvjWXGjNDBauDANTz33MKoKWe/V6NGLiNHLuPVV7/j6qt3k5dn5x//8HD55fE8/7yb7GyrE0px++wzJxMmeLDZggwfvpx69fSHfi6OFDSPx1Msr5+fn8+MGTMYP348I0aM4NFHH2X+/PkATJ06lTFjxhzNcK62b9/Oo48+yuLFi887X0ZGBo8++ijvvffeeb+GlB4qaHLO9uyx0a9fDIMGxXLggIMmTfbxj398T5cuW0rFbMfatXN46qklvPjij1x22V4OHrTz4ouhovbyy25yo7OflnpLl9p54IHQyM/dd6+lRYs9FieKPMVd0D788EN+/PFHqlSpQps2bWjfvj2NGzdm+/btLFu2jBtuuOG837tGjRpceumlzJo167xLXlpaGoA2f5ezooIm5+TTT51cc00cs2e7iI31cv/9K3n22UVUqXLI6mglrkGDTP7yl5957rkFXHrpPrKyQlv9XHllPO++68LvtzqhFJXUVBt9+sRSUGCjQ4dtdOmyxepIEelIsTl2MkBR2bNnD2vXrsUwDAYOHMhNN91Ehw4dqFy5Ml9++SUej4dWrVpd0Hu0bduWnJwcfvjhh/N6/pGtq6pXr35BOaR0UEGTsxIMwqRJbu67L5bsbDtXXLGH1177jo4dU0v97LXGjTOYMGER48f/hGEcYP9+OyNHxtCuXRw//VQKhhSjXE4O3HlnLPv22WnWLJ3Bg1eX+s/8+SrOa9A2btwIQNOmTY+7PT09nZSUFJo3b47L5bqg96hZsybJycksWrTovHYyODKCpoImZ0OTBOSMfD4YOdLDBx+4sduDDBq0mk6dtukgdQybLTSZoGnThSxcWIV//esS1qyJo0uXOLp08TJmTIE2aI9APh/cc08s69c7qF49h8cfXxrxM5OtVBwjaCtXruT9998/+vW0adOYNm0aACNGjOCXX34hGAzSrFmzkz7/zTffZMOGDfTr1++4chcMBvn4449ZsmQJbdq0oXPnzgA0b96cuXPnsmHDBho2bHjC6/n9fhYsWMDPP/9Meno6iYmJtGrVijZt2pCWlkbZsmVJTEw87/eX0kMjaHJaeXlw990xfPCBG7fbzxNPLOHmm1XOTsVmg2uu2c3rr39Lr14mbrePzz5z0apVHC+84CYvz+qEcraCQXjySQ/z5zspU6aAMWN+ISHBZ3WsiFYc16AlJibSvn17EhISsNvttG/f/uivpKQkUlJSsNvt1KpV66TPv+WWW7DZbMyePfu4UbGZM2eyZMkSWrRocVw5ql27NgAbNmw44bV8Ph+TJ0/ms88+w2azce2111KvXj3mzJnDtGnTyMnJOeH6s3N9fyk9NIImp5SRETq188svThISChk9+hcuuSTD6lgRweMJ0LNnCm3bbue99xrxww8XMXGih6lTnfzlL4V07uxTyQ1zkye7ePddN06nnyefXFIqr7MsaoWFoX13i7Kg1a5dm1q1avHNN99QuXJlOnTocPS+goICdu7cSXJy8infs1q1alx++eUsWbKEJUuWcNVVV/H111/z3Xff0axZM2677bbjHl+jRg0ANm/efMJrTZ8+nQ0bNtCxY0fatWuH7fBf8iuvvJLXX38dOPH05rm+v5QeGkGTk0pLs9G5c6icVap0iOefX6hydh6Sk/MZMWI5EyYs5OKLs0hLczBgQCzdusWydq3++oWrWbOcjB4dOqA/9NAKffaLSHHN4tyzZw9er/eE0ans7GwCgQBlypQ57fNvuukmnE4nc+fO5ccff2TWrFkYhkGvXr1O2MQ9NjYWp9NJZmbmcbenpqayePFi6tSpw4033ni0nAHUrVuXypUrAye//uxc3l9KD/3JywnWrrVz002xpKQ4qVUrm0mTFlKzptaOuBBNmhzg5Zd/ZMiQVSQkFLJggZMbbohj1CgPWVlWp5NjffaZkwEDYggEbPTsuYHWrXdaHSlqFFdBO9XF9wcPHgRCpep0ypUrx3XXXUdGRgYzZszg4osvpn///qfckD0uLu7oax/x448/AtCxY8dTPudkGc/n/aV0UEGT4yxc6OCWW2LZs8fBJZfs57nnfqJSJa2UXhQcjiCdOm3jrbe+4eabtwIwebKbVq3i+OQTJxG061rUmjrVyb33xuDz2ejadRM9e554nZGcv+IqaEeWr/j9CNqRWZs+35mvHTx2f88ePXqcdiKD1+s9YUaoaZrExcVRp06dkz5n//79JCYmUrZs2Qt+fykdVNDkqJkznfToEUNOjp2WLXfxzDOLSUjwWh0r6iQmehk8eDUvv/w9jRodID3dwQMPxHLrrTrtaaW333bx8MOxBAI2evc2ueuudbpOsIgV1zpoaWlp2Gw2qlWrdtztR0rP70e7fm/ZsmXMnDnz6OzK061zFggEyM/PP65Qeb1ecnNzKV++/HGnNo/YsmUL2dnZp1yg9lzeX0oPHQ0EgHfecTFwYAyFhXY6ddrKyJFLcbvPfZ0fOXu1a+fw3HMLefjhXylTpoDFi520bRvH6NEecnKsTle6vPyymyefDK3NNXDgGu64I0XlrBgcmSRQlOugBYNBdu7cSaVKlU543TJlypCQkEB6evopn79u3To+/vhjKleuzPDhw0lOTmbx4sXs2XPynSLS09MJBoPHlUG73Y7dbif3FNuIzJkzBzj56c1zfX8pPVTQhHfecfHEEzEEgzb69FnP4MGrS8WWTeHAboe2bdN4883Qac9gEN58003LlnFMn67TnsUtGITx491H99d84IEV2iWgmHi93qPLSBTlCFp6ejoFBQUnHZ2y2WzUqVOHgwcPsm/fvhPu37x5M++//z5ly5bl3nvvJSEhgY4dOxIIBPjf//530vfbtm0bAPXq1Tt6m8PhoFKlSmRlZbFmzZrjHj9//nxSUlKAEwva+by/lB4qaKXc//7nZNSo0PUg99+/kh49NmrkwAIJCT4GD17Niy/+QIMGGezd62Dw4NBsT9PUX9PiEAjAE094ePVVDw5HgOHDl9Ohw3arY0Wt/PzfrmUtymvQzrS/ZZMmTQBYv379cbfv3LmTd955h5iYGO69996jMz2bNWtGjRo1WLNmzUmX0jBNE7vdTuPGjY+7vW3btgC8//77TJ06lZkzZ/Lyyy8zZ84cypUrd0LG831/KT30k78U+/lnO4MHewgGbdx553o6dky1OlKpV69eNpMmLWDo0BUkJhawYIGTNm3iGDtWpz2Lks8HDz0Uw7/+5cbl8jNq1BKuu06zNYvTkdObULQF7Uz7WzZt2pTExESWLl169LZ9+/bx1ltvYbPZGDRoEJUqVTruOZ06dQJCi8UeKy8vj9WrV9OoUSPKly9/3H1XXHEFXbp0oWzZsixfvpwlS5ZQrlw5hg4dis1mIy4ujgoVKlzQ+0vpYgtG0DmU9PScyAl7BklJiaSnW3fE3bjRRqdOcWRm2unQYRv3379KI2dhJjvbxZQpDZk7tybBoI2kJD+jRnm54w6vTkFfgMJCGDIkhpkzXXg8PkaP/oVmzfZbHSvq7dy5kxdffBGAUaNGUbFixRJ773nz5vHll1/yyCOPXNA+mD/88AP//e9/uf/++085W1MuXEJCAo0bX251jCKRlJR43kdWjaCVQnv22Lj99lgyM+1ceeVuhgzR5s/hqEwZLw88sIoXXviRhg1Dsz0feSSG9u21Cfv5ysuDfv1imTnTRVxcIc88s1jlrIQU1ynOs3HddddRvnz5oxfrnw+v18v8+fNp2rSpypmUCBW0UiY3F3r1imH7dgf162cwYsRyHI6oGZiMSg0aZDFx4kIefXQZFSvmsWqVgy5d4hgwIIZt29Ssz1Zamo3u3WOZNy+0t+azzy6iUSPtEFBcUlNTefvtt/nPf/4DcHTlfbvdfnTR1pLicrno2bMn1atXP7rUx7k6cOAALVq04JZbbinidCInp2WKSxGvFwYOjGXVKidVqhzk6ad/ISbGb3UsOQs2G7RuvZMWLXYzY0ZdPv20LjNnupgzx8mQIYU89FAhxyzLJL8zY4aT4cM95OTYqVAhj2eeWazdMYpZfHw869evx+VycfXVV7Ns2TIgdKH8mbYv+uqrr1ixYgX79+/H5XLRqFEj/vznP5+wOOy5qFu3LnXr1j3v5/9+n0+R4qZr0CxS0tegBYPw8MMePvrITZkyBUyatIBq1bT5c6RKT49hypSGfPtt6Hqa5OQATz1VQI8ePrR132+ys+Hxx2P49NPQgf2qq3YzdOhKypUrPMMzpSi88847rF279rjb+vbtS7NmzU77vDlz5tCgQQPKli3Lvn37+Oijj7j22muPzpSU6KZr0EJU0CxS0gVt4kQ3L7zgwe32MWHCIgwj88xPkrC3fn053n67MRs2hGaUNW3q46mnCrn+en+pv65w0SIH993nIS3NgdvtY+DAtXTsmFrq/7+UpLy8PKZPn87atWupUKECHTp04NJLLz3n15k2bRo+n4+ePXsWQ0oJNypoISpoFinJgvZ//+di2LAY7PYgTz75C1ddtbdE3ldKRiAA339/Ee+915D9+0ObQl9xhY/hwwtp06b0FTWvFyZNcvPqq24CARt162YyfPhyqlc//XY/Eh4yMjL49ttv2bhxI1lZWfj9fnw+H23atDm6/IRENxW0EF2DFuW+/trBY4+FZkwNHrxK5SwK2e3QuvUOWrTYzcyZFzNjRh2WLPFwxx1O/vAHP8OHF9CuXekoaps22RgyJJZff3VgswXp3j2Fnj034HJFzb/totrBgwd55ZVXqFOnDrfccgvlypXDZrPxyiuvnHIhWpFopYIWxVassDNgQAx+v43u3VO46SYtRBvNYmL8dO++ic6dtzJrVi3+85+6LF/uoXfvOJo18/PoowV06BCdRS0YhA8+cDF6tIe8PBtJSYcYNuxXLr30gNXR5BysW7cOr9dLnz59jm46/ssvv1BQUHDCRugi0U4FLUplZED//rHk5dm54Ybt9OljWh1JSkhsrJ9u3TbTqdM2Zs+uyX/+U5cVK2Lo2zeOSy/1M2xYIZ06Rc9kgpQUO+PGuZkzJzQR4Prr0xg8eDUJCT6Lk8m5iouLo7CwkNWrV1O1alXWrVvHvHnz8Hg8J6y2LxLtdA2aRYrzGrRgEPr1i2H2bBf162fw/PMLdYqnFCsosDNnTi0+/bQOGRmha9QaNfJx//1ebr7ZR3y8xQHP0+LFDl57zcXs2aFiFhfnZciQVbRurS2bIlUwGGT69OksXboUl8tF8+bNcTgcbNu2jaFDh1odT0qIrkELUUGzSHEWtDfecPH00zHExxfyyis/ULlyXrG8j0SWwkI7X31Vg2nT6h2dTBAXF6BLFz89enhp2dIf9qNqgQDMmePkH/9w8csvoRMALpeftm3T6N49heTk/DO8goiEOxW0EBU0ixRXQVu2zE7nznH4fDZGjfqFli33FPl7SGTzeu3Mn1+dr76qgWn+tuFz9eoBevTw0r27l7p1w+uvWkEBfPqpi9dec7FxY2ibq/j4Qm6+eRudO2+hfHmtayYSLVTQQlTQLFIcBS0rC264IY7t2x3ccssWBg1aU6SvL9EnLS2eb76pzjffXER6+m/b71x+eWhU7U9/8lK+/GleoJhlZcH777t56y0Xe/eGhvcqVTpE165buPHGVGJjtROGSLRRQQtRQbNIURe0YBDuuiuGL790Ua9eJhMnLsTlChTZ60t0CwRg9eqKzJ9/EQsWVCU/P3Rdl8sV4IYb/Fx1VYDmzf00beqnbNniy5GfDytX2lm61MGSJXbmz3dw8GBoxKxWrUz+/OctXHvtTpzOqPlRICK/o4IWooJmkaIuaJMnuxg1Koa4OC+vvPIDVapoGyc5P/n5Dn76qQrz51dnxYpKBIPH/3ypUydU1po189O8eYAmTfzntQ9oMAipqTaWLnUc/bVqlR2v9/j3a9p0H7fdtok//CE9KpcIEZHjqaCFqKBZpCgL2ooVdjp1isXrtfP440u55ppdRfK6Ivv2xfDrr5XYuLEcKSll2bKlDF6v47jH2GxB6tb106xZgMTE0MbuZ/q1ZUuomKWn2094rZo1czCMTAwjg0suOaAdAERKGRW0EBU0ixRVQcvOhhtuiCU11cnNN29l8ODVRZBO5OS8XhupqYlHC9vGjWXZurUMfv/5Tf9MSCigQYMMLrkkE8PIpH79TOLjtX6ZSGmmghaihWojWDAIw4bFkJrqpE6dLO6+e63VkSTKuVxB6tbNpm7dbDp0CN1WWGhn69ZEtm4tg9drJxi0EQxy+Ffo93D878uVK6Bhw0yqVj2o05YiIiehghbB3nvPxeefu4iN9TJy5FLcbk0KkJLndgdo0CCLBg2yrI4iIhI1wnxZSjmVVavsjB7tBmDo0JVUq6ZJASIiItFCBS0C5ebCwIExFBba6dhxG3/8oyYFiIiIRBMVtAg0fHgMW7Y4uPjiLAYO1GK0IiIi0UYFLcJ8/rmT6dNdxMT4GDlyGR6PrjsTERGJNipoEWT/fhsjR3oAuPvutVofSkREJEqpoEWQJ5/0sH+/nSZN9tGhQ6rVcURERKSYqKBFiFmzQqc2PR4fQ4euxK4/ORERkailw3wEyMyExx4LLanRt69J1apaUkNERCSaqaBFgKefjmHvXgeNGh2gc+ctVscRERGRYqaCFubmzXPw8ccu3G4/Dz64Qqc2RURESgEd7sNYTg4MGxaatdm7t6lZmyIiIqWECloYGzvWw65dDurXz6BLF53aFBERKS1U0MLU9987+OADN05ngIceWonDEbQ6koiIiJQQFbQwlJsLDz8cmrV5xx0bqFUrx+JEIiIiUpJU0MLQhAke0tKc1K6dxW23bbI6joiIiJQwFbQws2iRg8mT3TgcAR5+eAVOp05tioiIlDYqaGHk0CF46KHQrM0//3kjdepkW5xIRERErKCCFkaef97Dli0OatbM5vbbN1odR0RERCyighYmli2z8+abLuz2IA89tAKXK2B1JBEREbGICloY8PthxIgYAgEbXbpspkGDLKsjiYiIiIVU0MLAlCkuVq50ULHiIXr23GB1HBEREbGYCprF9u2z8eyzoTXP7rlnHbGxfosTiYiIiNVU0Cw2fryb7Gw7f/jDXlq12mV1HBEREQkDKmgW+uUXO1OnhrZzuvfeNdhsVicSERGRcKCCZhG/H0aODK151rXrJi666KDFiURERCRcOM/mQYZhtAO6AXuBoGmaf/nd/e8AdY+5qSlwGZAEPAwsBwzgZ9M03z7mNe8AUoCGwDDTNDMu6LuJIG+8AatXO0lKOkSPHlrzTERERH5zxhE0wzDigDeAR0zTHAs0NQyj7e8eNtc0zdamabYGbgW+NU1zK1AVeMU0zReA+4CJhmFUMgzDAXwEjDRN83lgGTC2aL6l8JeebmPUqNA6Z/fcs5aYGE0MEBERkd+czQhaS2CbaZoFh79eANwMzDvyANM0/33M4wcA/zp8++e/ey0f4AUqADGmae4/fPtm4N5zTh+hnnkmNDHgssv20qLFbqvjiIiISJg5m4KWDOQc83X24dtOYBiGHegAvHySux8AJpimmXX4sTsMw2hsmuYa4CqgzJmClC8fh9PpOIvI4WvBAvj4Y3A6/ZoYICIichJJSYlWR7Dc2RS0vcCx/6fKHL7tZLoAX5imGTz2RsMwegHxpmmOP+bmTsA9hmHsIlT6Us8UJCPj0FnEDV8+HwwaFAc46Np1I9WqaWKAiIjI76Wn55z5QRHgQorm2czi/AmoZRiG5/DX1wD/MwyjgmEYvx/16g+8d+wNhmEMBJJN0xxvGEYTwzAaHL6rjGmaT5im+SqhEboPzvebiBTvvuti7VoH1aoVcttt2jFARERETu6MI2imaR4yDGMI8KphGOnAStM05xmGMRE4ADwHYBhGc2CDaZq5R55rGEYX4EVguWEYfwIqAkOBDcC9hmH4gG2AC5hYtN9aeNmzx8Zzz4U67mOP7cbj8XOWk2hFRESklLEFg8EzPypMpKfnRE7Y37n//himTXNx440+nnvOJDU1BadTBU1ERORYCQkJNG58udUxikRSUuJ5X2muhWpLwE8/OZg2zYXHE2T8+HxNDBAREZHTUkErZl4vPP546NTm0KGF1K4dsYOAIiIiUkJU0IrZv/7lYt06BzVrBhg6tNDqOCIiIhIBVNCK0b59NiZNCo2ePftsPrGxFgcSERGRiKCCVowmTnSTnW2jTRsf7dtrOycRERE5OypoxWTdOjtTprhwOIL85S8FmhggIiIiZ00FrRgEg/D00x4CARt9+3pp2DBgdSQRERGJICpoxeDrrx18952TMmWCjBihiQEiIiJyblTQipjXC2PGhCYGPPpoARUralkNEREROTcqaEXsvfdcbNzooHbtAAMGeK2OIyIiIhFIBa0IZWRwdFmNsWMLcLstDiQiIiIRSQWtCL3wgofMTBt//KOPjh19VscRERGRCKWCVkRSUuy8+64Luz3IuHFaVkNERETOnwpaERk71oPPZ6N3by+NG2tZDRERETl/KmhF4JtvHHz1lZOEhCAjR2pZDREREbkwKmgXyOf7bVmNhx8uJDlZy2qIiIjIhVFBu0AffOBi/XoHNWsGGDRIo2ciIiJy4VTQLkBWVmhDdIAxYwqIibE4kIiIiEQFFbQL8NJLHvbvt9OihY/OnbWshoiIiBQNFbTztHmzjcmTXdhsQZ55RstqiIiISNFRQTtPf/mLB6/Xxu23+2jWTMtqiIiISNFRQTsPCxc6mDXLRVxckFGjCqyOIyIiIlFGBe0cBQKhRWkBHnigkCpVtKyGiIiIFC0VtHM0Y4aTX391ULlygCFDtKyGiIiIFD0VtHOQnw8TJoRGzx5/vJD4eIsDiYiISFRSQTsHkye72L7dTqNGfu64w2t1HBEREYlSKmhn6cABePnl0OjZmDEFOBwWBxIREZGopYJ2ll56yUN2to3rr/fRpo3f6jgiIiISxVTQzsLmzTbefTe0KO2YMVqUVkRERIqXCtpZePbZ3xalvfRSLUorIiIixUsF7Qx+/tnOzJkuYmODPP64FqUVERGR4qeCdhrBIIwdGwPA4MGFVKumRWlFRESk+KmgncYXXzhZssRBpUoBhg7VorQiIiJSMlTQTqGwEJ55JrSsxmOPFZKQYHEgERERKTVU0E7hvfdcbN1qp359P3feqUVpRUREpOSooJ1EVha8+GJo9Gz06AJcLosDiYiISKmignYSL7/sISPDRqtWPjp00KK0IiIiUrJU0H4nNdXG5MmhIbOxY7UorYiIiJQ8FbTfmTDBQ0GBjW7dvDRvrkVpRUREpOSpoB1j9Wo706e7cLuDjBqlRWlFRETEGrZgUIuvioiIiIQTjaCJiIiIhBkVNBEREZEwo4ImIiIiEmZU0ERERETCjAqaiIiISJhRQRMREREJMypoIiIiImFGBU1EREQkzDitDlDaGIbxZ2A4EAvkAF1N00y3NpWIiIj1DMNoDQwwTbOP1VmsphG0kveNaZotTNNsBnwF9LA6kIiISJhoDiy3OkQ40AhayetvGMbtgAeoAoyyOI+IiEi4aAYcMAxjMZAE3G2a5rfWRrKGRtBKkGEYfYGrgBsOj6CZwBprU4mIiISN5kCOaZpXA4OBZyzOYxkVtJLVBFhommauYRi38f/t3D1qFWEUBuA3oE1Ip0024JGACJYpxEbskl5wC4K4ARFxAWmtUti6BRFBxMpgIQeCm5AUCnIt7q3NbcbvQ5+nmhnmwFu+nPlJDpN8GZwJAIarqitJriV5ubn0Ocn1cYnGov/hGgAAAPZJREFUUtD+rtMkj6vqfZIbSb5198XgTAAwg4Mk5939c3N+J8nZwDxD7axWq9EZAID/XFU9SvI8yc0kV7P+kO5Jd38cGmwQGzQAYAa3k7xO8iHJpyQn/0o5q6q3VXV/c/yiqk4um7FBAwBYUFXdzXo7+CrJwyRH3f3rTzMKGgDAwqrqXZK9JPe6+/tl93vECQCwoKq6lWQ/yY9tylmioAEALKaq9rN+t+44yUVVPdhmTkEDAFhAVe0meZPkaXd/zfrHu8+2mfUOGgDAZGzQAAAmo6ABAExGQQMAmIyCBgAwGQUNAGAyChoAwGQUNACAyShoAACT+Q1c3AQLs1rouAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(10, 6))\n",
    "plt.plot(x, y, 'b', linewidth=2)\n",
    "plt.ylim(bottom=0)\n",
    "Ix = np.linspace(a, b)\n",
    "Iy = f(Ix)\n",
    "verts = [(a, 0)] + list(zip(Ix, Iy)) + [(b, 0)]\n",
    "poly = Polygon(verts, facecolor='0.7', edgecolor='0.5')\n",
    "ax.add_patch(poly)\n",
    "plt.text(0.75 * (a + b), 1.5, r\"$\\int_a^b f(x)dx$\",\n",
    "         horizontalalignment='center', fontsize=20)\n",
    "plt.figtext(0.9, 0.075, '$x$')\n",
    "plt.figtext(0.075, 0.9, '$f(x)$')\n",
    "ax.set_xticks((a, b))\n",
    "ax.set_xticklabels(('$a$', '$b$'))\n",
    "ax.set_yticks([f(a), f(b)]);\n",
    "# plt.savefig('../../images/ch11/math_15.png');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Numerical Integration"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {
    "uuid": "6d3aa9c8-58c0-46a3-a89f-ca471a1f83e4"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "24.366995967084602"
      ]
     },
     "execution_count": 85,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sci.fixed_quad(f, a, b)[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {
    "uuid": "0ddebba6-5357-4ce9-b829-d752132d12df"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "24.374754718086752"
      ]
     },
     "execution_count": 86,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sci.quad(f, a, b)[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "metadata": {
    "uuid": "3b1779d6-c831-449d-964f-e2cc869847e7"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "24.374754718086713"
      ]
     },
     "execution_count": 87,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sci.romberg(f, a, b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "metadata": {
    "uuid": "5499809d-f2b1-4cc9-8808-511f4e82c5ed"
   },
   "outputs": [],
   "source": [
    "xi = np.linspace(0.5, 9.5, 25)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {
    "uuid": "aec239bc-cdd9-4477-b47c-4d0136ed686d"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "24.352733271544516"
      ]
     },
     "execution_count": 89,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sci.trapz(f(xi), xi)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "metadata": {
    "uuid": "ce33e420-5143-4d54-b23f-0040f54723fc"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "24.37496418455075"
      ]
     },
     "execution_count": 90,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sci.simps(f(xi), xi)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Integration by Simulation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {
    "uuid": "bb840eb2-0e13-40eb-aea7-0f106dcf9f41"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "24.804762279331463\n",
      "26.522918898332378\n",
      "26.265547519223976\n",
      "26.02770339943824\n",
      "24.99954181440844\n",
      "23.881810141621663\n",
      "23.527912274843253\n",
      "23.507857658961207\n",
      "23.67236746066989\n",
      "23.679410416062886\n",
      "24.424401707879305\n",
      "24.239005346819056\n",
      "24.115396924962802\n",
      "24.424191987566726\n",
      "23.924933080533783\n",
      "24.19484212027875\n",
      "24.117348378249833\n",
      "24.100690929662274\n",
      "23.76905109847816\n"
     ]
    }
   ],
   "source": [
    "for i in range(1, 20):\n",
    "    np.random.seed(1000)\n",
    "    x = np.random.random(i * 10) * (b - a) + a  \n",
    "    print(np.mean(f(x)) * (b - a))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Symbolic Computation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Basics"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {
    "uuid": "f01d358d-8094-426c-8e69-657218d8c319"
   },
   "outputs": [],
   "source": [
    "import sympy as sy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "metadata": {
    "uuid": "2cb7d5d8-ae45-4001-863e-714df216a656"
   },
   "outputs": [],
   "source": [
    "x = sy.Symbol('x')  \n",
    "y = sy.Symbol('y')  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "metadata": {
    "uuid": "7bf55a76-f348-4820-af94-a83ed233d9a2"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "sympy.core.symbol.Symbol"
      ]
     },
     "execution_count": 94,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "type(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "metadata": {
    "uuid": "a8f0388b-1df6-4389-877c-af5d9f141708"
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\sqrt{x}$"
      ],
      "text/plain": [
       "sqrt(x)"
      ]
     },
     "execution_count": 95,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sy.sqrt(x)  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "metadata": {
    "uuid": "f308fe2e-a5bc-4c88-a7f6-a4f09a568f2f"
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\sqrt{x} - 13$"
      ],
      "text/plain": [
       "sqrt(x) - 13"
      ]
     },
     "execution_count": 96,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "3 + sy.sqrt(x) - 4 ** 2  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "metadata": {
    "uuid": "025f5084-4efc-4416-a564-b8a96ec426fd"
   },
   "outputs": [],
   "source": [
    "f = x ** 2 + 3 + 0.5 * x ** 2 + 3 / 2  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "metadata": {
    "uuid": "f427581e-50ba-45b9-a145-ff734be26e59"
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle 1.5 x^{2} + 4.5$"
      ],
      "text/plain": [
       "1.5*x**2 + 4.5"
      ]
     },
     "execution_count": 98,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sy.simplify(f)  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "metadata": {
    "uuid": "59837e7c-a82f-44e5-8b87-b0fba310ffc5"
   },
   "outputs": [],
   "source": [
    "sy.init_printing(pretty_print=False, use_unicode=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 100,
   "metadata": {
    "uuid": "ea1bbb85-a431-4e6c-a264-6ffb6df9f59e"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "     2      \n",
      "1.5*x  + 4.5\n"
     ]
    }
   ],
   "source": [
    "print(sy.pretty(f))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 101,
   "metadata": {
    "uuid": "e8702014-5347-4eac-b10c-39c5a54459c9"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "  ___      \n",
      "\\/ x  + 0.5\n"
     ]
    }
   ],
   "source": [
    "print(sy.pretty(sy.sqrt(x) + 0.5))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 102,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 253 ms, sys: 8.23 ms, total: 262 ms\n",
      "Wall time: 262 ms\n"
     ]
    }
   ],
   "source": [
    "%time pi_str = str(sy.N(sy.pi, 400000))  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 103,
   "metadata": {
    "uuid": "b8cf7cf4-56e2-4c6b-a70b-6592ec4bd6a6"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'3.1415926535897932384626433832795028841971'"
      ]
     },
     "execution_count": 103,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pi_str[:42]  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 104,
   "metadata": {
    "uuid": "595cc15e-99b8-43c7-ad89-db4500fdb860"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'8245672736856312185020980470362464176199'"
      ]
     },
     "execution_count": 104,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pi_str[-40:]  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 105,
   "metadata": {
    "uuid": "cc4b85c4-e603-4d36-9553-f3999e877fca"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 94 µs, sys: 1e+03 ns, total: 95 µs\n",
      "Wall time: 97 µs\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "80847"
      ]
     },
     "execution_count": 105,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%time pi_str.find('061072')  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Equations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 106,
   "metadata": {
    "uuid": "c310eeab-ac04-4015-a327-29628f9a9a11"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[-1, 1]"
      ]
     },
     "execution_count": 106,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sy.solve(x ** 2 - 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 107,
   "metadata": {
    "uuid": "60076f9d-93f3-47e0-b5b6-87d1bca3d30a"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[-2, 2]"
      ]
     },
     "execution_count": 107,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sy.solve(x ** 2 - 1 - 3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 108,
   "metadata": {
    "uuid": "6c9e1060-61e6-4b18-9be4-cb71b83fc5a7"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[0.858094329496553, -0.679047164748276 - 0.839206763026694*I, -0.679047164748276 + 0.839206763026694*I]"
      ]
     },
     "execution_count": 108,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sy.solve(x ** 3 + 0.5 * x ** 2 - 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 109,
   "metadata": {
    "uuid": "fcd70615-0db5-4c5c-8246-245ba3c8501c"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[{x: -I*y}, {x: I*y}]"
      ]
     },
     "execution_count": 109,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sy.solve(x ** 2 + y ** 2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Integration and Differentiation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 110,
   "metadata": {
    "uuid": "503329d1-812a-461c-9019-e6bb2a44125e"
   },
   "outputs": [],
   "source": [
    "a, b = sy.symbols('a b')  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 111,
   "metadata": {},
   "outputs": [],
   "source": [
    "I = sy.Integral(sy.sin(x) + 0.5 * x, (x, a, b))  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 112,
   "metadata": {
    "uuid": "af7bf980-d65b-4567-8576-404e79c5ac65"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "  b                    \n",
      "  /                    \n",
      " |                     \n",
      " |  (0.5*x + sin(x)) dx\n",
      " |                     \n",
      "/                      \n",
      "a                      \n"
     ]
    }
   ],
   "source": [
    "print(sy.pretty(I))  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 113,
   "metadata": {
    "uuid": "89d4c980-01d7-423a-a2ab-a9698787019a"
   },
   "outputs": [],
   "source": [
    "int_func = sy.integrate(sy.sin(x) + 0.5 * x, x)  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 114,
   "metadata": {
    "uuid": "38141163-7d29-4bd6-bfaf-9f9cfad86967"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "      2         \n",
      "0.25*x  - cos(x)\n"
     ]
    }
   ],
   "source": [
    "print(sy.pretty(int_func))  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 115,
   "metadata": {
    "uuid": "51d4481a-c6b6-4caa-b4d1-aa6fb04d4493"
   },
   "outputs": [],
   "source": [
    "Fb = int_func.subs(x, 9.5).evalf()  \n",
    "Fa = int_func.subs(x, 0.5).evalf()  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 116,
   "metadata": {
    "uuid": "0c46e097-c665-440e-9d05-03c0d6e6d8d8"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "24.3747547180867"
      ]
     },
     "execution_count": 116,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Fb - Fa  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 117,
   "metadata": {},
   "outputs": [],
   "source": [
    "int_func_limits = sy.integrate(sy.sin(x) + 0.5 * x, (x, a, b))  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 118,
   "metadata": {
    "uuid": "657b13dc-101e-4c0c-9d15-43dbd418c3c8"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "        2         2                  \n",
      "- 0.25*a  + 0.25*b  + cos(a) - cos(b)\n"
     ]
    }
   ],
   "source": [
    "print(sy.pretty(int_func_limits))  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 119,
   "metadata": {
    "uuid": "5c65cea8-1e15-4efa-aba4-52888becaf19"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "24.3747547180868"
      ]
     },
     "execution_count": 119,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "int_func_limits.subs({a : 0.5, b : 9.5}).evalf()  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 120,
   "metadata": {
    "uuid": "b13767c8-4878-42c1-b738-0727b824b329"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "24.3747547180867"
      ]
     },
     "execution_count": 120,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sy.integrate(sy.sin(x) + 0.5 * x, (x, 0.5, 9.5))  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Differentiation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 121,
   "metadata": {
    "uuid": "6ea93bb3-eb7c-4837-8327-621f3752b657"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.5*x + sin(x)"
      ]
     },
     "execution_count": 121,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "int_func.diff()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 122,
   "metadata": {
    "uuid": "164131fd-a197-40ce-85d6-94221e808073"
   },
   "outputs": [],
   "source": [
    "f = (sy.sin(x) + 0.05 * x ** 2\n",
    "   + sy.sin(y) + 0.05 * y ** 2)  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 123,
   "metadata": {
    "uuid": "5d1ce51b-2536-469b-b516-56db1e86519a"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.1*x + cos(x)"
      ]
     },
     "execution_count": 123,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "del_x = sy.diff(f, x)  \n",
    "del_x  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 124,
   "metadata": {
    "uuid": "8d778c21-ed6a-43f0-8347-b95af334972a"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.1*y + cos(y)"
      ]
     },
     "execution_count": 124,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "del_y = sy.diff(f, y)  \n",
    "del_y  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 125,
   "metadata": {
    "uuid": "588daaba-266a-43da-a4b9-baeb56fc1ac8"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-1.42755177876459"
      ]
     },
     "execution_count": 125,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "xo = sy.nsolve(del_x, -1.5)  \n",
    "xo  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 126,
   "metadata": {
    "uuid": "2ef9beca-58f2-470b-a50e-6292bffbf2e0"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-1.42755177876459"
      ]
     },
     "execution_count": 126,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "yo = sy.nsolve(del_y, -1.5)  \n",
    "yo  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 127,
   "metadata": {
    "uuid": "c0812b29-c69f-4a30-aaf1-1447d1434cf4"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-1.77572565314742"
      ]
     },
     "execution_count": 127,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f.subs({x : xo, y : yo}).evalf()  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 128,
   "metadata": {
    "uuid": "fd89d904-eab3-4035-941a-785c6a3f36cb"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.74632928225285"
      ]
     },
     "execution_count": 128,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "xo = sy.nsolve(del_x, 1.5)\n",
    "xo"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 129,
   "metadata": {
    "uuid": "cc99d8f4-e062-4c7e-85ae-46e96d3c8f19"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.74632928225285"
      ]
     },
     "execution_count": 129,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "yo = sy.nsolve(del_y, 1.5)  \n",
    "yo"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 130,
   "metadata": {
    "uuid": "54622abe-cef1-47ff-bf23-b883cf588a91"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.27423381055640"
      ]
     },
     "execution_count": 130,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f.subs({x : xo, y : yo}).evalf()  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<img src=\"http://hilpisch.com/tpq_logo.png\" alt=\"The Python Quants\" width=\"35%\" align=\"right\" border=\"0\"><br>\n",
    "\n",
    "<a href=\"http://tpq.io\" target=\"_blank\">http://tpq.io</a> | <a href=\"http://twitter.com/dyjh\" target=\"_blank\">@dyjh</a> | <a href=\"mailto:training@tpq.io\">training@tpq.io</a>"
   ]
  }
 ],
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   "codemirror_mode": {
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